Theorem inegd 1392

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 115	. 2 |- ( ph -> ( ps -> F. ) )
3		dfnot 1391	. 2 |- ( -. ps <-> ( ps -> F. ) )
4	2, 3	sylibr 134	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   F. wfal 1378

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379

This theorem is referenced by:  genpdisj  7638  cauappcvgprlemdisj  7766  caucvgprlemdisj  7789  caucvgprprlemdisj  7817  suplocexprlemdisj  7835  suplocexprlemub  7838  suplocsrlem  7923  resqrexlemgt0  11364  resqrexlemoverl  11365  leabs  11418  climge0  11669  isprm5lem  12496  ennnfonelemex  12818  dedekindeu  15128  dedekindicclemicc  15137  pw1nct  15977