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Axiom ax-14 1339
 Description: Axiom of Equality. One of the equality and substitution axioms for a non-logical predicate in our predicate calculus with equality. It substitutes equal variables into the right-hand side of the ∈ binary predicate. Axiom scheme C13' in [Megill] p. 448 (p. 16 of the preprint). It is a special case of Axiom B8 (p. 75) of system S2 of [Tarski] p. 77. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-14 (x = y → (z xz y))

Detailed syntax breakdown of Axiom ax-14
StepHypRef Expression
1 vx . . 3 set x
2 vy . . 3 set y
31, 2weq 1326 . 2 wff x = y
4 vz . . . 4 set z
54, 1wel 1328 . . 3 wff z x
64, 2wel 1328 . . 3 wff z y
75, 6wi 4 . 2 wff (z xz y)
83, 7wi 4 1 wff (x = y → (z xz y))
 Colors of variables: wff set class This axiom is referenced by:  elequ2  1514
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