Theorem alequcoms 1409

Description: A commutation rule for identical variable specifiers. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
alequcoms.1	|- ( A. x x = y -> ph )

Assertion

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

Proof of Theorem alequcoms

Step	Hyp	Ref	Expression
1		alequcom 1408	. 2 |- ( A. y y = x -> A. x x = y )
2		alequcoms.1	. 2 |- ( A. x x = y -> ph )
3	1, 2	syl 14	1 |- ( A. y y = x -> ph )

Syntax hints:   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-10 1396

This theorem is referenced by:  hbae  1606  dral1  1618  drex1  1679  aev  1693  sbequi  1720