Theorem naecoms 2081

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 2079	. 2 |- ( A. x x = y <-> A. y y = x )
2		naecoms.1	. 2 |- ( -. A. x x = y -> ph )
3	1, 2	sylnbir 307	1 |- ( -. A. y y = x -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1405

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-12 1880  ax-13 2028

This theorem depends on definitions:  df-bi 187  df-an 371  df-ex 1636  df-nf 1640

This theorem is referenced by:  sb9  2195  eujustALT  2243  nfcvf2  2592  axpowndlem2  9007  wl-sbcom2d  31391  wl-mo2dnae  31399