Theorem nan 514

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 276	. 2 |- (((ph /\ ps) -> -. ch) <-> (ph -> (ps -> -. ch)))
2		imnan 207	. . 3 |- ((ps -> -. ch) <-> -. (ps /\ ch))
3	2	imbi2i 160	. 2 |- ((ph -> (ps -> -. ch)) <-> (ph -> -. (ps /\ ch)))
4	1, 3	bitr2 152	1 |- ((ph -> -. (ps /\ ch)) <-> ((ph /\ ps) -> -. ch))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127   /\ wa 196

This theorem is referenced by:  cfsuc 3709

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

This theorem depends on definitions:  df-bi 128  df-an 198

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