Theorem notornotel2 33898

Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)

Hypothesis

Ref	Expression
notornotel2.1	|- ( ph -> -. ( ps \/ -. ch ) )

Assertion

Ref	Expression
notornotel2	|- ( ph -> ch )

Proof of Theorem notornotel2

Step	Hyp	Ref	Expression
1		notornotel2.1	. . 3 |- ( ph -> -. ( ps \/ -. ch ) )
2		orcom 402	. . 3 |- ( ( -. ch \/ ps ) <-> ( ps \/ -. ch ) )
3	1, 2	sylnibr 319	. 2 |- ( ph -> -. ( -. ch \/ ps ) )
4	3	notornotel1 33897	1 |- ( ph -> 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:  ac6s6  33980