Theorem nalequcoms 1504

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 1502	. . 3 |- (A.x x = y -> A.y y = x)
2		nalequcoms.1	. . 3 |- (-. A.x x = y -> ph)
3	1, 2	nsyl4 135	. 2 |- (-. ph -> A.y y = x)
4	3	con1i 112	1 |- (-. A.y y = x -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 1296   = wceq 1298

This theorem is referenced by:  sbcom 1632  ax11inda2ALT 1760  eujustALT 1774  ralcom2 2244  ralcom2OLD 2245  dfid3 3587  nd5 6094  axrepndlem1 6096  axrepndlem2 6097  axrepnd 6098  axpowndlem3 6103  axpownd 6105

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-10 1308

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