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Theorem nabi1 24828
Description: Constructor theorem for  -/\. (Contributed by Anthony Hart, 1-Sep-2011.)
Assertion
Ref Expression
nabi1  |-  ( (
ph 
<->  ps )  ->  (
( ph  -/\  ch )  <->  ( ps  -/\  ch )
) )

Proof of Theorem nabi1
StepHypRef Expression
1 anbi1 687 . . 3  |-  ( (
ph 
<->  ps )  ->  (
( ph  /\  ch )  <->  ( ps  /\  ch )
) )
21notbid 285 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ( ph  /\  ch ) 
<->  -.  ( ps  /\  ch ) ) )
3 df-nan 1288 . 2  |-  ( (
ph  -/\  ch )  <->  -.  ( ph  /\  ch ) )
4 df-nan 1288 . 2  |-  ( ( ps  -/\  ch )  <->  -.  ( ps  /\  ch ) )
52, 3, 43bitr4g 279 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  -/\  ch )  <->  ( ps  -/\  ch )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358    -/\ wnan 1287
This theorem is referenced by:  nabi1i  24830
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-nan 1288
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