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Theorem axc11nlem 1938
Description: Lemma for axc11n 2049. Change bound variable in an equality. (Contributed by NM, 8-Jul-2016.) (Proof shortened by Wolf Lammen, 17-Feb-2018.) Restructure to ease either bundling, or reducing dependencies on axioms. (Revised by Wolf Lammen, 30-Nov-2019.)
Hypothesis
Ref Expression
axc11nlem.1
Assertion
Ref Expression
axc11nlem
Distinct variable groups:   ,   ,

Proof of Theorem axc11nlem
StepHypRef Expression
1 cbvaev 1817 . . 3
2 equequ2 1799 . . . . 5
32biimprd 223 . . . 4
43al2imi 1636 . . 3
51, 4syl5com 30 . 2
6 axc11nlem.1 . . . . 5
76spsd 1867 . . . 4
87com12 31 . . 3
98con1d 124 . 2
105, 9pm2.61d 158 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393
This theorem is referenced by:  aevlem1  1939  axc11n  2049
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-12 1854
This theorem depends on definitions:  df-bi 185  df-ex 1613
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