Theorem axc11rvOLD 2140

Description: Obsolete proof of axc11rv 2139 as of 11-Oct-2021. (Contributed by BJ, 6-Jul-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc11rvOLD	|- ( A. x x = y -> ( A. y ph -> A. x ph ) )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem axc11rvOLD

Step	Hyp	Ref	Expression
1		ax12v2 2049	. . . 4 |- ( x = y -> ( ph -> A. x ( x = y -> ph ) ) )
2	1	sps 2055	. . 3 |- ( A. x x = y -> ( ph -> A. x ( x = y -> ph ) ) )
3		pm2.27 42	. . . 4 |- ( x = y -> ( ( x = y -> ph ) -> ph ) )
4	3	al2imi 1743	. . 3 |- ( A. x x = y -> ( A. x ( x = y -> ph ) -> A. x ph ) )
5	2, 4	syld 47	. 2 |- ( A. x x = y -> ( ph -> A. x ph ) )
6	5	spsd 2057	1 |- ( A. x x = y -> ( A. y ph -> A. x ph ) )

Syntax hints:   -> 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-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  axc16gOLD  2161