Users' Mathboxes Mathbox for Wolf Lammen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-nanbi2 Structured version   Unicode version

Theorem wl-nanbi2 31820
Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.) (Revised by Wolf Lammen, 27-Jun-2020.)
Assertion
Ref Expression
wl-nanbi2  |-  ( (
ph 
<->  ps )  ->  (
( ph  -/\  ch )  <->  ( ps  -/\  ch )
) )

Proof of Theorem wl-nanbi2
StepHypRef Expression
1 imbi1 324 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ph  ->  -.  ch ) 
<->  ( ps  ->  -.  ch ) ) )
2 wl-dfnan2 31815 . 2  |-  ( (
ph  -/\  ch )  <->  ( ph  ->  -.  ch ) )
3 wl-dfnan2 31815 . 2  |-  ( ( ps  -/\  ch )  <->  ( ps  ->  -.  ch )
)
41, 2, 33bitr4g 291 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  -/\  ch )  <->  ( ps  -/\  ch )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    -/\ wnan 1379
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 188  df-an 372  df-nan 1380
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator