Theorem ax13dgen1 2014

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

Assertion

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

Proof of Theorem ax13dgen1

Step	Hyp	Ref	Expression
1		equid 1939	. 2 |- x = x
2	1	pm2.24i 146	1 |- ( -. x = x -> ( x = z -> A. x x = z ) )

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-ex 1705

This theorem is referenced by:  ax13dgen4OLD  2018