Users' Mathboxes Mathbox for Wolf Lammen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-nancom Structured version   Visualization version   Unicode version

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
StepHypRef 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 ) )
41, 2, 33bitr4i 281 1  |-  ( (
ph  -/\  ps )  <->  ( ps  -/\  ph ) )
Colors of variables: wff setvar class
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)
  Copyright terms: Public domain W3C validator