MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax13dgen4OLD Structured version   Visualization version   Unicode version

Theorem ax13dgen4OLD 2018
Description: Obsolete proof of ax13dgen4 2017 as of 10-Oct-2021. (Contributed by NM, 13-Apr-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax13dgen4OLD  |-  ( -.  x  =  x  -> 
( x  =  x  ->  A. x  x  =  x ) )

Proof of Theorem ax13dgen4OLD
StepHypRef Expression
1 ax13dgen1 2014 1  |-  ( -.  x  =  x  -> 
( x  =  x  ->  A. x  x  =  x ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1481
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935
This theorem depends on definitions:  df-bi 197  df-ex 1705
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator