Theorem nalequcoms 1143

Description: A commutation rule for distinct variable specifiers.

Hypothesis

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

Assertion

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

Proof of Theorem nalequcoms

Step	Hyp	Ref	Expression
1		alequcom 1141	. . 3 |- (A.x x = y -> A.y y = x)
2		nalequcoms.1	. . 3 |- (-. A.x x = y -> ph)
3	1, 2	nsyl4 120	. 2 |- (-. ph -> A.y y = x)
4	3	con1i 96	1 |- (-. A.y y = x -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 953   = wceq 955

This theorem is referenced by:  sbcom 1257  ax11inda2ALT 1368  ralcom2 1774  dfid3 2832  nd5 4925  axrepndlem1 4927  axrepndlem2 4928  axrepnd 4929  axpowndlem3 4934  axpownd 4936

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-10 965

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