Theorem alcom 1502

Description: Theorem 19.5 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
alcom	|- ( A. x A. y ph <-> A. y A. x ph )

Proof of Theorem alcom

Step	Hyp	Ref	Expression
1		ax-7 1472	. 2 |- ( A. x A. y ph -> A. y A. x ph )
2		ax-7 1472	. 2 |- ( A. y A. x ph -> A. x A. y ph )
3	1, 2	impbii 126	1 |- ( A. x A. y ph <-> A. y A. x ph )

Syntax hints:   <-> wb 105   A.wal 1371

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-7 1472

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  alrot3  1509  alrot4  1510  nfalt  1602  nfexd  1785  sbnf2  2010  sbcom2v  2014  sbalyz  2028  sbal1yz  2030  sbal2  2049  2eu4  2149  ralcomf  2669  gencbval  2826  unissb  3894  dfiin2g  3974  dftr5  4161  cotr  5083  cnvsym  5085  dffun2  5300  funcnveq  5356  fun11  5360