Theorem intnanrd 694

Description: Introduction of conjunct inside of a contradiction.

Hypothesis

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

Assertion

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

Proof of Theorem intnanrd

Step	Hyp	Ref	Expression
1		intnand.1	. 2 |- (ph -> -. ps)
2		pm3.26 319	. 2 |- ((ps /\ ch) -> ps)
3	1, 2	nsyl 116	1 |- (ph -> -. (ps /\ ch))

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

This theorem is referenced by:  axrepnd 4946  ltxrltt 5500  dffsum 6998  dfisum 7191  ruclem28 7537  intn3an1d 10428  intn3an2d 10429

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