Metamath Proof Explorer


Theorem ax13dgen2

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

Ref Expression
Assertion ax13dgen2
|- ( -. x = y -> ( y = x -> A. x y = x ) )

Proof

Step Hyp Ref Expression
1 equcomi
 |-  ( y = x -> x = y )
2 pm2.21
 |-  ( -. x = y -> ( x = y -> A. x y = x ) )
3 1 2 syl5
 |-  ( -. x = y -> ( y = x -> A. x y = x ) )