Theorem inegd 1350

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 114	. 2 |- ( ph -> ( ps -> F. ) )
3		dfnot 1349	. 2 |- ( -. ps <-> ( ps -> F. ) )
4	2, 3	sylibr 133	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   F. wfal 1336

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337

This theorem is referenced by:  genpdisj  7324  cauappcvgprlemdisj  7452  caucvgprlemdisj  7475  caucvgprprlemdisj  7503  suplocexprlemdisj  7521  suplocexprlemub  7524  suplocsrlem  7609  resqrexlemgt0  10785  resqrexlemoverl  10786  leabs  10839  climge0  11087  ennnfonelemex  11916  dedekindeu  12759  dedekindicclemicc  12768