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Axiom ax-i12 1331
Description: Axiom of Quantifier Introduction. One of the equality and substitution axioms of predicate calculus with equality. Informally, it says that whenever is distinct from and , and is true, then quantified with is also true. In other words, is irrelevant to the truth of . Axiom scheme C9' in [Megill] p. 448 (p. 16 of the preprint). It apparently does not otherwise appear in the literature but is easily proved from textbook predicate calculus by cases.

This axiom has been modified from the original ax-12 1335 for compatibility with intuitionistic logic. (Contributed by Mario Carneiro, 31-Jan-2015.)

Assertion
Ref Expression
ax-i12

Detailed syntax breakdown of Axiom ax-i12
StepHypRef Expression
1 vz . . . 4
2 vx . . . 4
31, 2weq 1325 . . 3
43, 1wal 1266 . 2
5 vy . . . . 5
61, 5weq 1325 . . . 4
76, 1wal 1266 . . 3
82, 5weq 1325 . . . . 5
98, 1wal 1266 . . . . 5
108, 9wi 4 . . . 4
1110, 1wal 1266 . . 3
127, 11wo 608 . 2
134, 12wo 608 1
Colors of variables: wff set class
This axiom is referenced by:  ax-12  1335  ax12or  1336  dveeq2  1582  dveeq2or  1583  dvelimALT  1761  dvelimfv  1762
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