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Axiom ax-c14 2222
 Description: Axiom of Quantifier Introduction. One of the equality and substitution axioms for a non-logical predicate in our predicate calculus with equality. Axiom scheme C14' in [Megill] p. 448 (p. 16 of the preprint). It is redundant if we include ax-5 1704; see theorem axc14 2113. Alternately, ax-5 1704 becomes unnecessary in principle with this axiom, but we lose the more powerful metalogic afforded by ax-5 1704. We retain ax-c14 2222 here to provide completeness for systems with the simpler metalogic that results from omitting ax-5 1704, which might be easier to study for some theoretical purposes. This axiom is obsolete and should no longer be used. It is proved above as theorem axc14 2113. (Contributed by NM, 24-Jun-1993.) (New usage is discouraged.)
Assertion
Ref Expression
ax-c14

Detailed syntax breakdown of Axiom ax-c14
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, 6wel 1819 . . . 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:  ax5el  2267  ax12el  2272
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