Theorem wl-nancom 31864

Description: The 'nand' operator commutes. (Contributed by Mario Carneiro, 9-May-2015.) (Revised by Wolf Lammen, 26-Jun-2020.)

Assertion

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

Proof of Theorem wl-nancom

Step	Hyp	Ref	Expression
1		con2b 336	. 2 |- ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )
2		wl-dfnan2 31863	. 2 |- ( ( ph -/\ ps ) <-> ( ph -> -. ps ) )
3		wl-dfnan2 31863	. 2 |- ( ( ps -/\ ph ) <-> ( ps -> -. ph ) )
4	1, 2, 3	3bitr4i 281	1 |- ( ( ph -/\ ps ) <-> ( ps -/\ ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 188   -/\ wnan 1386

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 189  df-an 373  df-nan 1387

This theorem is referenced by: (None)