Theorem ax12a2OLD 2343

Description: Obsolete proof of ax12v 2048 as of 24-Mar-2021. (Contributed by NM, 12-Feb-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ax12a2OLD.1	|- ( x = z -> ( A. z ph -> A. x ( x = z -> ph ) ) )

Assertion

Ref	Expression
ax12a2OLD	|- ( -. A. x x = y -> ( x = y -> ( ph -> A. x ( x = y -> ph ) ) ) )

Distinct variable groups:   x, z   y, z   ph, z

Allowed substitution hints:   ph( x, y)

Proof of Theorem ax12a2OLD

Step	Hyp	Ref	Expression
1		ax12v 2048	. 2 |- ( x = z -> ( ph -> A. x ( x = z -> ph ) ) )
2	1	ax12v2OLD 2342	1 |- ( -. A. x x = y -> ( x = y -> ( ph -> A. x ( x = y -> ph ) ) ) )

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  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  axc15OLD  2344