Theorem unitresl 33884

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

Hypotheses

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

Assertion

Ref	Expression
unitresl	|- ( ph -> ps )

Proof of Theorem unitresl

Step	Hyp	Ref	Expression
1		unitresl.1	. 2 |- ( ph -> ( ps \/ ch ) )
2		unitresl.2	. 2 |- ( ph -> -. ch )
3		orcom 402	. . 3 |- ( ( ps \/ ch ) <-> ( ch \/ ps ) )
4		df-or 385	. . 3 |- ( ( ch \/ ps ) <-> ( -. ch -> ps ) )
5	3, 4	sylbb 209	. 2 |- ( ( ps \/ ch ) -> ( -. ch -> ps ) )
6	1, 2, 5	sylc 65	1 |- ( ph -> ps )

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:  unitresr  33885