Equivalence calculus of First order logic for discrete Mathematics--3.2

3.2 First-order logical equivalence calculus
• 3.2.1 First-order logical equivalents and permutation rules
– Basic equivalence type
– Substitution rules, rules for changing names, substitution rules
• 3.2.2 First-order logical front-beam paradigm

Negative words come out from inside and come in from both sides, quantifier symbols change

The quantifier is assigned the same time. No allocation rate in the same direction.

US (full name designation Rule Universal specify)
ES (existence of specified rules exstential specify)
UG (full name promotion Rule Universal Generalize)
EG (existence promotion rule existential Generalize)
P Rule (Premise) additional Prerequisites
T Rule (transformation)
CP Rules (Conclusion Premise)

The theorem of CP proposition deduction (CP rule)

EG existence Promotion Rule (existence quantifier introduction rule)

ES existence quantifier specified rule (existence quantifier elimination rule)

UG Full name Promotion rule (Universal quantifier introduction rule)

US full name refers to rules (universal quantifier elimination rule)

The power set of set A is the set of all subsets of a.  multiplication is the Cartesian product. Cartesian product is ordered to

The compound of r0s relationship and relationship

One of the most commonly used methods of indirect proof-CP rules

Equivalence calculus of First order logic for discrete Mathematics--3.2