Theorem naecoms 2146

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		aecom 2144	. 2 |- ( A. x x = y <-> A. y y = x )
2		naecoms.1	. 2 |- ( -. A. x x = y -> ph )
3	1, 2	sylnbir 309	1 |- ( -. A. y y = x -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1441

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932  ax-13 2090

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667

This theorem is referenced by:  sb9  2254  eujustALT  2301  nfcvf2  2615  axpowndlem2  9020  wl-sbcom2d  31884  wl-mo2df  31892  wl-eudf  31894