Theorem unitresr 33885

Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Hypotheses

Ref	Expression
unitresr.1	|- ( ph -> ( ps \/ ch ) )
unitresr.2	|- ( ph -> -. ps )

Assertion

Ref	Expression
unitresr	|- ( ph -> ch )

Proof of Theorem unitresr

Step	Hyp	Ref	Expression
1		unitresr.1	. . 3 |- ( ph -> ( ps \/ ch ) )
2	1	orcomd 403	. 2 |- ( ph -> ( ch \/ ps ) )
3		unitresr.2	. 2 |- ( ph -> -. ps )
4	2, 3	unitresl 33884	1 |- ( ph -> ch )

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

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

This theorem is referenced by: (None)