Theorem alequcoms 1509

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 1508	. 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 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-10 1498

This theorem is referenced by:  hbae  1711  dral1  1723  drex1  1791  aev  1805  sbequi  1832