Theorem intn3an3d 1383

Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

Hypothesis

Ref	Expression
intn3and.1	|- ( ph -> -. ps )

Assertion

Ref	Expression
intn3an3d	|- ( ph -> -. ( ch /\ th /\ ps ) )

Proof of Theorem intn3an3d

Step	Hyp	Ref	Expression
1		intn3and.1	. 2 |- ( ph -> -. ps )
2		simp3 1011	. 2 |- ( ( ch /\ th /\ ps ) -> ps )
3	1, 2	nsyl 125	1 |- ( ph -> -. ( ch /\ th /\ ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ w3a 986

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 189  df-an 373  df-3an 988

This theorem is referenced by:  en3lp  8126  winainflem  9123  spthispth  25315  2spotdisj  25801  gtnelioc  37597  icccncfext  37775  fourierdlem10  37989