Theorem notnotd 639

Description: Deduction associated with notnot 638 and notnoti 654. (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 638	. 2 |- ( ps -> -. -. ps )
3	1, 2	syl 14	1 |- ( ph -> -. -. ps )

This proof depends on syntax axioms:   -. wn 3   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 623  ax-in2 624

This theorem is used by:  ismkvnex  7495  exmidonfinlem  7545  xqltnle  10702  mod2eq1n2dvds  12646  bits0e  12716  bitsmod  12723  pceq0  13101  birthdaylem3  16089  eupth2lembfi  16718