Theorem wl-nannan 33298

Description: Lemma for handling nested 'nand's. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Revised by Wolf Lammen, 26-Jun-2020.)

Assertion

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

Proof of Theorem wl-nannan

Step	Hyp	Ref	Expression
1		wl-dfnan2 33296	. 2 |- ( ( ph -/\ ( ps -/\ ch ) ) <-> ( ph -> -. ( ps -/\ ch ) ) )
2		nanan 1449	. . 3 |- ( ( ps /\ ch ) <-> -. ( ps -/\ ch ) )
3	2	imbi2i 326	. 2 |- ( ( ph -> ( ps /\ ch ) ) <-> ( ph -> -. ( ps -/\ ch ) ) )
4	1, 3	bitr4i 267	1 |- ( ( ph -/\ ( ps -/\ ch ) ) <-> ( ph -> ( ps /\ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ wa 384   -/\ wnan 1447

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 197  df-an 386  df-nan 1448

This theorem is referenced by: (None)