Theorem nannan 1291

Description: Lemma for handling nested 'nand's. (Contributed by Jeff Hoffman, 19-Nov-2007.)

Assertion

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

Proof of Theorem nannan

Step	Hyp	Ref	Expression
1		df-nan 1288	. . 3 |- ((ph -/\ (ch -/\ ps)) <-> -. (ph /\ (ch -/\ ps)))
2		df-nan 1288	. . . 4 |- ((ch -/\ ps) <-> -. (ch /\ ps))
3	2	anbi2i 675	. . 3 |- ((ph /\ (ch -/\ ps)) <-> (ph /\ -. (ch /\ ps)))
4	1, 3	xchbinx 301	. 2 |- ((ph -/\ (ch -/\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
5		iman 413	. 2 |- ((ph -> (ch /\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
6	4, 5	bitr4i 243	1 |- ((ph -/\ (ch -/\ ps)) <-> (ph -> (ch /\ ps)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358   -/\ wnan 1287

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 177  df-an 360  df-nan 1288

This theorem is referenced by:  nanim  1292  nic-mp  1436  nic-ax  1438