Theorem cnf1dd 33892

Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)

Hypotheses

Ref	Expression
cnf1dd.1	|- ( ph -> ( ps -> -. ch ) )
cnf1dd.2	|- ( ph -> ( ps -> ( ch \/ th ) ) )

Assertion

Ref	Expression
cnf1dd	|- ( ph -> ( ps -> th ) )

Proof of Theorem cnf1dd

Step	Hyp	Ref	Expression
1		cnf1dd.1	. . 3 |- ( ph -> ( ps -> -. ch ) )
2		cnf1dd.2	. . 3 |- ( ph -> ( ps -> ( ch \/ th ) ) )
3	1, 2	jcad 555	. 2 |- ( ph -> ( ps -> ( -. ch /\ ( ch \/ th ) ) ) )
4		df-or 385	. . 3 |- ( ( ch \/ th ) <-> ( -. ch -> th ) )
5		pm3.35 611	. . 3 |- ( ( -. ch /\ ( -. ch -> th ) ) -> th )
6	4, 5	sylan2b 492	. 2 |- ( ( -. ch /\ ( ch \/ th ) ) -> th )
7	3, 6	syl6 35	1 |- ( ph -> ( ps -> th ) )

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:  cnf2dd  33893  cnfn1dd  33894  mpt2bi123f  33971  mptbi12f  33975  ac6s6  33980