Theorem aecoms 2312

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 2311	. 2 |- ( A. y y = x <-> A. x x = y )
2		aecoms.1	. 2 |- ( A. x x = y -> ph )
3	1, 2	sylbi 207	1 |- ( A. y y = x -> ph )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  axc11  2314  nd4  9412  axrepnd  9416  axpownd  9423  axregnd  9426  axinfnd  9428  axacndlem5  9433  axacnd  9434  wl-ax11-lem1  33362  wl-ax11-lem3  33364  wl-ax11-lem9  33370  wl-ax11-lem10  33371  e2ebind  38779