Theorem inegd 1308

Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

Ref	Expression
inegd.1	|- ( ( ph /\ ps ) -> F. )

Assertion

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

Proof of Theorem inegd

Step	Hyp	Ref	Expression
1		inegd.1	. . 3 |- ( ( ph /\ ps ) -> F. )
2	1	ex 113	. 2 |- ( ph -> ( ps -> F. ) )
3		dfnot 1307	. 2 |- ( -. ps <-> ( ps -> F. ) )
4	2, 3	sylibr 132	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 102   F. wfal 1294

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295

This theorem is referenced by:  genpdisj  7082  cauappcvgprlemdisj  7210  caucvgprlemdisj  7233  caucvgprprlemdisj  7261  resqrexlemgt0  10453  resqrexlemoverl  10454  leabs  10507  climge0  10713