Theorem nan 691

Description: Theorem to move a conjunct in and out of a negation.

Assertion

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

Proof of Theorem nan

Step	Hyp	Ref	Expression
1		impexp 347	. 2 |- (((ph /\ ps) -> -. ch) <-> (ph -> (ps -> -. ch)))
2		imnan 242	. . 3 |- ((ps -> -. ch) <-> -. (ps /\ ch))
3	2	imbi2i 185	. 2 |- ((ph -> (ps -> -. ch)) <-> (ph -> -. (ps /\ ch)))
4	1, 3	bitr2 174	1 |- ((ph -> -. (ps /\ ch)) <-> ((ph /\ ps) -> -. ch))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  alephval3 4914  efilcp 10556  efilcp2 10561

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