MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax4sp1 Unicode version

Theorem ax4sp1 2126
Description: A special case of ax-4 2087 without using ax-4 2087 or ax-17 1606. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax4sp1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 2125 . 2  |-  -.  A. y  -.  x  =  x
21pm2.21i 123 1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-8 1661  ax-6o 2089  ax-9o 2090
  Copyright terms: Public domain W3C validator