Theorem aecoms 2111

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 2110	. 2 |- ( A. y y = x <-> A. x x = y )
2		aecoms.1	. 2 |- ( A. x x = y -> ph )
3	1, 2	sylbi 198	1 |- ( A. y y = x -> ph )

Syntax hints:   -> wi 4   A.wal 1435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057

This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662

This theorem is referenced by:  axc11  2113  nd4  9022  axrepnd  9026  axpownd  9033  axregnd  9036  axinfnd  9038  axacndlem5  9043  axacnd  9044  wl-ax11-lem1  31879  wl-ax11-lem3  31881  wl-ax11-lem9  31887  wl-ax11-lem10  31888  e2ebind  36900