Theorem naecoms 2313

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 2311	. 2 |- ( A. x x = y <-> A. y y = x )
2		naecoms.1	. 2 |- ( -. A. x x = y -> ph )
3	1, 2	sylnbir 321	1 |- ( -. A. y y = x -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  sb9  2426  eujustALT  2473  nfcvf2  2789  axpowndlem2  9420  wl-sbcom2d  33344  wl-mo2df  33352  wl-eudf  33354