Theorem intn3an2d 1443

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
intn3an2d	|- ( ph -> -. ( ch /\ ps /\ th ) )

Proof of Theorem intn3an2d

Step	Hyp	Ref	Expression
1		intn3and.1	. 2 |- ( ph -> -. ps )
2		simp2 1062	. 2 |- ( ( ch /\ ps /\ th ) -> ps )
3	1, 2	nsyl 135	1 |- ( ph -> -. ( ch /\ ps /\ th ) )

Syntax hints:   -. wn 3   -> wi 4   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  iooelexlt  33210  lenelioc  39763  icccncfext  40100  fourierdlem10  40334  fourierdlem104  40427  cznnring  41956