Theorem con3dimp 644

Description: Variant of con3d 640 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
con3dimp.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
con3dimp	|- ( ( ph /\ -. ch ) -> -. ps )

Proof of Theorem con3dimp

Step	Hyp	Ref	Expression
1		con3dimp.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	con3d 640	. 2 |- ( ph -> ( -. ch -> -. ps ) )
3	2	imp 124	1 |- ( ( ph /\ -. ch ) -> -. ps )

This proof depends on syntax axioms:   -. wn 3   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-in1 623  ax-in2 624

This theorem is used by:  stoic1a  1476  nelneq  2339  nelneq2  2340  nelss  3309  eqsndc  7216  nnnninf  7472  bcpasc  11225  fiinfnf1o  11246  swrdccat  11528  nnoddn2prmb  13069  pcprod  13153  lgsdir  16376  2lgslem2  16433  2lgs  16445  pw1nct  17255