Theorem cnfn2dd

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

	Ref	Expression
Hypotheses	cnfn2dd.1	|- ( ph -> ( ps -> th ) )
	cnfn2dd.2	|- ( ph -> ( ps -> ( ch \/ -. th ) ) )
Assertion	cnfn2dd	|- ( ph -> ( ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		cnfn2dd.1	|- ( ph -> ( ps -> th ) )
2		cnfn2dd.2	|- ( ph -> ( ps -> ( ch \/ -. th ) ) )
3		notnot	|- ( th -> -. -. th )
4	1 3	syl6	|- ( ph -> ( ps -> -. -. th ) )
5	4 2	cnf2dd	|- ( ph -> ( ps -> ch ) )