Theorem nancom 1290

Description: The 'nand' operator commutes. (Contributed by Mario Carneiro, 9-May-2015.)

Assertion

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

Proof of Theorem nancom

Step	Hyp	Ref	Expression
1		ancom 437	. . 3 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	notbii 287	. 2 |- (-. (ph /\ ps) <-> -. (ps /\ ph))
3		df-nan 1288	. 2 |- ((ph -/\ ps) <-> -. (ph /\ ps))
4		df-nan 1288	. 2 |- ((ps -/\ ph) <-> -. (ps /\ ph))
5	2, 3, 4	3bitr4i 268	1 |- ((ph -/\ ps) <-> (ps -/\ ph))

Syntax hints:  -. wn 3   <-> 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:  nanbi2  1296  falnantru  1356  nincom  3227