Theorem biortn 395

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		notnot1 114	. 2 |- (ph -> -. -. ph)
2		biorf 394	. 2 |- (-. -. ph -> (ps <-> (-. ph \/ ps)))
3	1, 2	syl 15	1 |- (ph -> (ps <-> (-. ph \/ ps)))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  oranabs  829