Theorem inegd 1383

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 1382	. 2 |- ( -. ps <-> ( ps -> F. ) )
4	2, 3	sylibr 134	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   F. wfal 1369

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 1367  df-fal 1370

This theorem is referenced by:  genpdisj  7590  cauappcvgprlemdisj  7718  caucvgprlemdisj  7741  caucvgprprlemdisj  7769  suplocexprlemdisj  7787  suplocexprlemub  7790  suplocsrlem  7875  resqrexlemgt0  11185  resqrexlemoverl  11186  leabs  11239  climge0  11490  isprm5lem  12309  ennnfonelemex  12631  dedekindeu  14859  dedekindicclemicc  14868  pw1nct  15647