Theorem inegd 1333

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 423	. 2 |- (ph -> (ps -> F. ))
3		dfnot 1332	. 2 |- (-. ps <-> (ps -> F. ))
4	2, 3	sylibr 203	1 |- (ph -> -. ps)

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358   F. wfal 1317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-fal 1320

This theorem is referenced by:  efald  1334