Theorem ax13dgen2 2015

Description: Degenerate instance of ax-13 2246 where bundled variables x and z have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)

Assertion

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

Proof of Theorem ax13dgen2

Step	Hyp	Ref	Expression
1		equcomi 1944	. 2 |- ( y = x -> x = y )
2		pm2.21 120	. 2 |- ( -. x = y -> ( x = y -> A. x y = x ) )
3	1, 2	syl5 34	1 |- ( -. x = y -> ( y = x -> A. x y = x ) )

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-an 386  df-ex 1705

This theorem is referenced by: (None)