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Axiom ax-c9 2221
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This axiom is obsolete and should no longer be used. It is proved above as theorem axc9 2046. (Contributed by NM, 10-Jan-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c9

Detailed syntax breakdown of Axiom ax-c9
StepHypRef Expression
1 vz . . . . 5
2 vx . . . . 5
31, 2weq 1733 . . . 4
43, 1wal 1393 . . 3
54wn 3 . 2
6 vy . . . . . 6
71, 6weq 1733 . . . . 5
87, 1wal 1393 . . . 4
98wn 3 . . 3
102, 6weq 1733 . . . 4
1110, 1wal 1393 . . . 4
1210, 11wi 4 . . 3
139, 12wi 4 . 2
145, 13wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  hbae-o  2232  ax13fromc9  2235  equid1  2237  hbequid  2239  equid1ALT  2255  dvelimf-o  2259  ax5eq  2262
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