Theorem biortn 664

Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012.)

Assertion

Ref	Expression
biortn	|- ( ph -> ( ps <-> ( -. ph \/ ps ) ) )

Proof of Theorem biortn

Step	Hyp	Ref	Expression
1		notnot 559	. 2 |- ( ph -> -. -. ph )
2		biorf 663	. 2 |- ( -. -. ph -> ( ps <-> ( -. ph \/ ps ) ) )
3	1, 2	syl 14	1 |- ( ph -> ( ps <-> ( -. ph \/ ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 98   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  oranabs  728