Theorem bicom1 131

Description: Commutative law for equivalence. (Contributed by Wolf Lammen, 10-Nov-2012.)

Assertion

Ref	Expression
bicom1	|- ( ( ph <-> ps ) -> ( ps <-> ph ) )

Proof of Theorem bicom1

Step	Hyp	Ref	Expression
1		biimpr 130	. 2 |- ( ( ph <-> ps ) -> ( ps -> ph ) )
2		biimp 118	. 2 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
3	1, 2	impbid 129	1 |- ( ( ph <-> ps ) -> ( ps <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  bicomi  132  bicom  140  pm5.21ndd  706  cbvexdh  1941  elabgf2  15436