Theorem atbiffatnnb 41079

Description: If a implies b, then a implies not not b. (Contributed by Jarvin Udandy, 28-Aug-2016.)

Assertion

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

Proof of Theorem atbiffatnnb

Step	Hyp	Ref	Expression
1		idd 24	. . 3 |- ( ph -> ( ps -> ps ) )
2		notnotb 304	. . 3 |- ( ps <-> -. -. ps )
3	1, 2	syl6ib 241	. 2 |- ( ph -> ( ps -> -. -. ps ) )
4	3	a2i 14	1 |- ( ( ph -> ps ) -> ( ph -> -. -. ps ) )

Syntax hints:   -. wn 3   -> wi 4

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

This theorem is referenced by:  atbiffatnnbalt  41081