Theorem cnf1dd

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

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

Proof

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