Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  axc11nlem Structured version   Visualization version   Unicode version

Theorem axc11nlem 2021
 Description: Lemma for axc11n 2143. 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 1886 . . 3
2 equequ2 1868 . . . . 5
32biimprd 227 . . . 4
43al2imi 1687 . . 3
51, 4syl5com 31 . 2
6 axc11nlem.1 . . . . 5
76spsd 1945 . . . 4
87com12 32 . . 3
98con1d 128 . 2
105, 9pm2.61d 162 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1442 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664 This theorem is referenced by:  aevlem1  2022  axc11n  2143
 Copyright terms: Public domain W3C validator