MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax12dgen3 Unicode version

Theorem ax12dgen3 1701
Description: Degenerate instance of ax-12 1866 where bundled variables  y and  z have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax12dgen3  |-  ( -.  x  =  y  -> 
( y  =  y  ->  A. x  y  =  y ) )

Proof of Theorem ax12dgen3
StepHypRef Expression
1 equid 1644 . . 3  |-  y  =  y
21ax-gen 1533 . 2  |-  A. x  y  =  y
32a1ii 24 1  |-  ( -.  x  =  y  -> 
( y  =  y  ->  A. x  y  =  y ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
  Copyright terms: Public domain W3C validator