Theorem nalequcoms 1144

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 1142	. . 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 954   = wceq 956

This theorem is referenced by:  sbcom 1258  ax11inda2ALT 1369  ralcom2 1776  dfid3 2836  nd5 4942  axrepndlem1 4944  axrepndlem2 4945  axrepnd 4946  axpowndlem3 4951  axpownd 4953

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-10 966

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