Theorem nalequcoms 1510

Description: A commutation rule for distinct variable specifiers. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 2-Feb-2015.)

Hypothesis

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

Assertion

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

Proof of Theorem nalequcoms

Step	Hyp	Ref	Expression
1		alequcom 1508	. . 3 |- ( A. x x = y -> A. y y = x )
2	1	con3i 627	. 2 |- ( -. A. y y = x -> -. A. x x = y )
3		nalequcoms.1	. 2 |- ( -. A. x x = y -> ph )
4	2, 3	syl 14	1 |- ( -. A. y y = x -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1346   = wceq 1348

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 609  ax-in2 610  ax-10 1498

This theorem is referenced by:  nd5  1811