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Theorem axc9lem2 2040
Description: Lemma for nfeqf2 2041. This lemma is equivalent to ax13v 2000 with one distinct variable constraint removed. (Contributed by Wolf Lammen, 8-Sep-2018.) (New usage is discouraged.)
Assertion
Ref Expression
axc9lem2
Distinct variable group:   ,

Proof of Theorem axc9lem2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 axc9lem1 2001 . . . 4
2 equequ2 1799 . . . . . . 7
32biimprcd 225 . . . . . 6
43eximi 1656 . . . . 5
5 19.36v 1762 . . . . 5
64, 5sylib 196 . . . 4
71, 6syl9 71 . . 3
87alrimdv 1721 . 2
9 nfv 1707 . . 3
109, 2equsal 2036 . 2
118, 10syl6ib 226 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393  E.wex 1612
This theorem is referenced by:  nfeqf2  2041
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-10 1837  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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