Theorem orsird 33890

Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Hypothesis

Ref	Expression
orsird.1	|- ( ph -> -. ( ps \/ ch ) )

Assertion

Ref	Expression
orsird	|- ( ph -> -. ch )

Proof of Theorem orsird

Step	Hyp	Ref	Expression
1		orsird.1	. . 3 |- ( ph -> -. ( ps \/ ch ) )
2		ioran 511	. . 3 |- ( -. ( ps \/ ch ) <-> ( -. ps /\ -. ch ) )
3	1, 2	sylib 208	. 2 |- ( ph -> ( -. ps /\ -. ch ) )
4	3	simprd 479	1 |- ( ph -> -. ch )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386

This theorem is referenced by: (None)