Theorem aecoms 2072

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 2071	. 2 |- ( A. y y = x <-> A. x x = y )
2		aecoms.1	. 2 |- ( A. x x = y -> ph )
3	1, 2	sylbi 195	1 |- ( A. y y = x -> ph )

Syntax hints:   -> wi 4   A.wal 1397

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1633  ax-4 1646  ax-5 1719  ax-6 1765  ax-7 1808  ax-10 1855  ax-12 1872  ax-13 2020

This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1628  df-nf 1632

This theorem is referenced by:  axc11  2074  nd4  8900  axrepnd  8904  axpownd  8911  axregnd  8914  axregndOLD  8915  axinfnd  8917  axacndlem5  8922  axacnd  8923  wl-ax11-lem1  30230  wl-ax11-lem3  30232  wl-ax11-lem9  30238  wl-ax11-lem10  30239  e2ebind  33715