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Axiom ax-11 1370
Description: Axiom of Variable Substitution. One of the 5 equality axioms of predicate calculus. The final consequent is a way of expressing " substituted for in wff " (cf. sb6 1739). It is based on Lemma 16 of [Tarski] p. 70 and Axiom C8 of [Monk2] p. 105, from which it can be proved by cases.

Variants of this axiom which are equivalent in classical logic but which have not been shown to be equivalent for intuitionistic logic are ax11v 1681, ax11v2 1674 and ax-11o 1677. (Contributed by NM, 5-Aug-1993.)

Assertion
Ref Expression
ax-11

Detailed syntax breakdown of Axiom ax-11
StepHypRef Expression
1 vx . . 3  setvar
2 vy . . 3  setvar
31, 2weq 1365 . 2
4 wph . . . 4
54, 2wal 1221 . . 3
63, 4wi 4 . . . 4
76, 1wal 1221 . . 3
85, 7wi 4 . 2
93, 8wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  ax10o  1576  equs5a  1648  sbcof2  1664  ax11o  1676  ax11v  1681
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