Theorem cnf2dd

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

	Ref	Expression
Hypotheses	cnf2dd.1	|- ( ph -> ( ps -> -. th ) )
	cnf2dd.2	|- ( ph -> ( ps -> ( ch \/ th ) ) )
Assertion	cnf2dd	|- ( ph -> ( ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		cnf2dd.1	|- ( ph -> ( ps -> -. th ) )
2		cnf2dd.2	|- ( ph -> ( ps -> ( ch \/ th ) ) )
3		pm1.4	|- ( ( ch \/ th ) -> ( th \/ ch ) )
4	2 3	syl6	|- ( ph -> ( ps -> ( th \/ ch ) ) )
5	1 4	cnf1dd	|- ( ph -> ( ps -> ch ) )