Theorem nancom 1450

Description: The 'nand' operator commutes. (Contributed by Mario Carneiro, 9-May-2015.) (Proof shortened by Wolf Lammen, 7-Mar-2020.)

Assertion

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

Proof of Theorem nancom

Step	Hyp	Ref	Expression
1		df-nan 1448	. . 3 |- ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
2		ancom 466	. . 3 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
3	1, 2	xchbinx 324	. 2 |- ( ( ph -/\ ps ) <-> -. ( ps /\ ph ) )
4		df-nan 1448	. 2 |- ( ( ps -/\ ph ) <-> -. ( ps /\ ph ) )
5	3, 4	bitr4i 267	1 |- ( ( ph -/\ ps ) <-> ( ps -/\ ph ) )

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-an 386  df-nan 1448

This theorem is referenced by:  nanbi2  1456  falnantru  1526  rp-fakenanass  37860