Theorem wl-nannot 33299

Description: Show equivalence between negation and the Nicod version. To derive nic-dfneg 1595, apply nanbi 1454. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Revised by Wolf Lammen, 26-Jun-2020.)

Assertion

Ref	Expression
wl-nannot	|- ( -. ph <-> ( ph -/\ ph ) )

Proof of Theorem wl-nannot

Step	Hyp	Ref	Expression
1		wl-dfnan2 33296	. 2 |- ( ( ph -/\ ph ) <-> ( ph -> -. ph ) )
2		pm4.8 380	. 2 |- ( ( ph -> -. ph ) <-> -. ph )
3	1, 2	bitr2i 265	1 |- ( -. ph <-> ( ph -/\ ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   -/\ 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)