Theorem nanan 1449

Description: Write 'and' in terms of 'nand'. (Contributed by Mario Carneiro, 9-May-2015.)

Assertion

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

Proof of Theorem nanan

Step	Hyp	Ref	Expression
1		df-nan 1448	. 2 |- ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
2	1	con2bii 347	1 |- ( ( ph /\ ps ) <-> -. ( ph -/\ ps ) )

Syntax hints:   -. wn 3   <-> 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-nan 1448

This theorem is referenced by:  nannan  1451  wl-nannan  33298