Theorem biort 819

Description: A disjunction with a true formula is equivalent to that true formula. (Contributed by NM, 23-May-1999.)

Assertion

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

Proof of Theorem biort

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ph -> ph )
2		orc 702	. 2 |- ( ph -> ( ph \/ ps ) )
3	1, 2	2thd 174	1 |- ( ph -> ( ph <-> ( ph \/ ps ) ) )

Syntax hints:   -> wi 4   <-> wb 104   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.55dc  903