Theorem biortn 696

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 591	. 2 |- ( ph -> -. -. ph )
2		biorf 695	. 2 |- ( -. -. ph -> ( ps <-> ( -. ph \/ ps ) ) )
3	1, 2	syl 14	1 |- ( ph -> ( ps <-> ( -. ph \/ ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 103   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  oranabs  761