MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  equs5 Unicode version

Theorem equs5 2092
Description: Lemma used in proofs of substitution properties. (Contributed by NM, 14-May-1993.) (Revised by BJ, 1-Oct-2018.)
Assertion
Ref Expression
equs5

Proof of Theorem equs5
StepHypRef Expression
1 nfna1 1903 . . 3
2 nfa1 1897 . . 3
3 axc15 2085 . . . 4
43impd 431 . . 3
51, 2, 4exlimd 1914 . 2
6 equs4 2035 . 2
75, 6impbid1 203 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612
This theorem is referenced by:  sb3  2096  sb4  2097
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
  Copyright terms: Public domain W3C validator