Theorem aecoms 2012

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 2011	. 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 1368

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794  ax-13 1955

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591

This theorem is referenced by:  axc11  2014  nd4  8866  axrepnd  8870  axpowndlem3OLD  8877  axpownd  8879  axregnd  8882  axregndOLD  8883  axinfnd  8885  axacndlem5  8890  axacnd  8891  wl-ax11-lem1  28550  wl-ax11-lem3  28552  wl-ax11-lem9  28558  wl-ax11-lem10  28559  e2ebind  31605