Theorem notnotd 631

Description: Deduction associated with notnot 630 and notnoti 646. (Contributed by Jarvin Udandy, 2-Sep-2016.) Avoid biconditional. (Revised by Wolf Lammen, 27-Mar-2021.)

Hypothesis

Ref	Expression
notnotd.1	|- ( ph -> ps )

Assertion

Ref	Expression
notnotd	|- ( ph -> -. -. ps )

Proof of Theorem notnotd

Step	Hyp	Ref	Expression
1		notnotd.1	. 2 |- ( ph -> ps )
2		notnot 630	. 2 |- ( ps -> -. -. ps )
3	1, 2	syl 14	1 |- ( ph -> -. -. ps )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 615  ax-in2 616

This theorem is referenced by:  ismkvnex  7221  exmidonfinlem  7260  xqltnle  10357  mod2eq1n2dvds  12044  bits0e  12113  pceq0  12491