Theorem naecoms 1948

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

Hypothesis

Ref	Expression
nalequcoms.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 1946	. . 3 |- (A.x x = y -> A.y y = x)
2		nalequcoms.1	. . 3 |- (-. A.x x = y -> ph)
3	1, 2	nsyl4 134	. 2 |- (-. ph -> A.y y = x)
4	3	con1i 121	1 |- (-. A.y y = x -> ph)

Syntax hints:  -. wn 3   -> wi 4  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  eujustALT  2207  nfcvf2  2513