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Theorem axc14 2113
Description: Axiom ax-c14 2222 is redundant if we assume ax-5 1704. Remark 9.6 in [Megill] p. 448 (p. 16 of the preprint), regarding axiom scheme C14'.

Note that is a dummy variable introduced in the proof. Its purpose is to satisfy the distinct variable requirements of dveel2 2112 and ax-5 1704. By the end of the proof it has vanished, and the final theorem has no distinct variable requirements. (Contributed by NM, 29-Jun-1995.) (Proof modification is discouraged.)

Assertion
Ref Expression
axc14

Proof of Theorem axc14
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 hbn1 1838 . . . . 5
2 dveel2 2112 . . . . 5
31, 2hbim1 1918 . . . 4
4 elequ1 1821 . . . . 5
54imbi2d 316 . . . 4
63, 5dvelim 2079 . . 3
7 nfa1 1897 . . . . 5
87nfn 1901 . . . 4
9819.21 1905 . . 3
106, 9syl6ib 226 . 2
1110pm2.86d 99 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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