MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  axc16g Unicode version

Theorem axc16g 1940
Description: Generalization of axc16 1941. Use the latter when sufficient. (Contributed by NM, 15-May-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 18-Feb-2018.) Remove dependency on ax-13 1999, along an idea of BJ. (Revised by Wolf Lammen, 30-Nov-2019.)
Assertion
Ref Expression
axc16g
Distinct variable group:   ,

Proof of Theorem axc16g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 aevlem1 1939 . 2
2 ax-5 1704 . 2
3 axc112 1937 . 2
41, 2, 3syl2im 38 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393
This theorem is referenced by:  axc16  1941  ax16gb  1942  aev  1943  aevOLD  2062  ax16nfALT  2065
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
  Copyright terms: Public domain W3C validator