Theorem cnf2dd 33893

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

Hypotheses

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

Assertion

Ref	Expression
cnf2dd	|- ( ph -> ( ps -> ch ) )

Proof of Theorem cnf2dd

Step	Hyp	Ref	Expression
1		cnf2dd.1	. 2 |- ( ph -> ( ps -> -. th ) )
2		cnf2dd.2	. . 3 |- ( ph -> ( ps -> ( ch \/ th ) ) )
3	2	orcomdd 33891	. 2 |- ( ph -> ( ps -> ( th \/ ch ) ) )
4	1, 3	cnf1dd 33892	1 |- ( ph -> ( ps -> ch ) )

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  df-an 386

This theorem is referenced by:  cnfn2dd  33895  mpt2bi123f  33971  mptbi12f  33975  ac6s6  33980