Theorem cnfn1dd 33894

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

Hypotheses

Ref	Expression
cnfn1dd.1	|- ( ph -> ( ps -> ch ) )
cnfn1dd.2	|- ( ph -> ( ps -> ( -. ch \/ th ) ) )

Assertion

Ref	Expression
cnfn1dd	|- ( ph -> ( ps -> th ) )

Proof of Theorem cnfn1dd

Step	Hyp	Ref	Expression
1		cnfn1dd.1	. . 3 |- ( ph -> ( ps -> ch ) )
2		notnot 136	. . 3 |- ( ch -> -. -. ch )
3	1, 2	syl6 35	. 2 |- ( ph -> ( ps -> -. -. ch ) )
4		cnfn1dd.2	. 2 |- ( ph -> ( ps -> ( -. ch \/ th ) ) )
5	3, 4	cnf1dd 33892	1 |- ( ph -> ( ps -> th ) )

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:  mpt2bi123f  33971  mptbi12f  33975  ac6s6  33980