Theorem naecoms 1724

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

Hypothesis

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

Assertion

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

Proof of Theorem naecoms

Step	Hyp	Ref	Expression
1		ax-10 1505	. . 3 |- ( A. x x = y -> A. y y = x )
2	1	con3i 632	. 2 |- ( -. A. y y = x -> -. A. x x = y )
3		naecoms.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 1351   = wceq 1353

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 614  ax-in2 615  ax-10 1505

This theorem is referenced by:  nfcvf2  2343