Metamath Proof Explorer


Theorem ax13dgen1

Description: Degenerate instance of ax-13 where bundled variables x and y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017)

Ref Expression
Assertion ax13dgen1
|- ( -. x = x -> ( x = z -> A. x x = z ) )

Proof

Step Hyp Ref Expression
1 equid
 |-  x = x
2 1 pm2.24i
 |-  ( -. x = x -> ( x = z -> A. x x = z ) )