Theorem ax12dgen 2011

Description: Degenerate instance of ax-12 2047 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
ax12dgen	|- ( x = x -> ( A. x ph -> A. x ( x = x -> ph ) ) )

Proof of Theorem ax12dgen

Step	Hyp	Ref	Expression
1		ala1 1741	. 2 |- ( A. x ph -> A. x ( x = x -> ph ) )
2	1	a1i 11	1 |- ( x = x -> ( A. x ph -> A. x ( x = x -> ph ) ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1722  ax-4 1737

This theorem is referenced by: (None)