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Axiom ax-14 1732
Description: Axiom of Right Equality for Binary Predicate. 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 an arbitrary binary predicate e., which we will use for the set membership relation when set theory is introduced. This axiom scheme is a sub-scheme of Axiom Scheme B8 of system S2 of [Tarski], p. 75, whose general form cannot be represented with our notation. Also appears as Axiom scheme C13' in [Megill] p. 448 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-14

Detailed syntax breakdown of Axiom ax-14
StepHypRef Expression
1 vx . . 3
2 vy . . 3
31, 2weq 1655 . 2
4 vz . . . 4
54, 1wel 1729 . . 3
64, 2wel 1729 . . 3
75, 6wi 4 . 2
83, 7wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  elequ2  1733  el  4420  dtru  4429  fv3  5787  elirrv  7614  ax10ext  27762
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