Theorem aecoms 2157

Description: A commutation rule for identical variable specifiers. (Contributed by NM, 10-May-1993.)

Hypothesis

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

Assertion

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

Proof of Theorem aecoms

Step	Hyp	Ref	Expression
1		aecom 2156	. 2 |- ( A. y y = x <-> A. x x = y )
2		aecoms.1	. 2 |- ( A. x x = y -> ph )
3	1, 2	sylbi 200	1 |- ( A. y y = x -> ph )

Syntax hints:   -> wi 4   A.wal 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-10 1926  ax-12 1944  ax-13 2102

This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675  df-nf 1679

This theorem is referenced by:  axc11  2159  nd4  9046  axrepnd  9050  axpownd  9057  axregnd  9060  axinfnd  9062  axacndlem5  9067  axacnd  9068  wl-ax11-lem1  31961  wl-ax11-lem3  31963  wl-ax11-lem9  31969  wl-ax11-lem10  31970  e2ebind  36975