Theorem intnand 693

Description: Introduction of conjunct inside of a contradiction.

Hypothesis

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

Assertion

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

Proof of Theorem intnand

Step	Hyp	Ref	Expression
1		intnand.1	. 2 |- (ph -> -. ps)
2		pm3.27 323	. 2 |- ((ch /\ ps) -> ps)
3	1, 2	nsyl 116	1 |- (ph -> -. (ch /\ ps))

Syntax hints:  -. wn 2   -> wi 3   /\ wa 223

This theorem is referenced by:  ixp0 4361  cfsuc 4915  ltxrltt 5500  abssubne0t 6882  intn3an2d 10429  intn3an3d 10430  cdrci 10494

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain