Theorem inegd 1263

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 108	. 2 |- ( ph -> ( ps -> F. ) )
3		dfnot 1262	. 2 |- ( -. ps <-> ( ps -> F. ) )
4	2, 3	sylibr 137	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97   F. wfal 1248

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  genpdisj  6621  cauappcvgprlemdisj  6749  caucvgprlemdisj  6772  caucvgprprlemdisj  6800  resqrexlemgt0  9618  resqrexlemoverl  9619  leabs  9672  climge0  9845