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Theorem nabi2 24901
Description: Constructor theorem for  -/\. (Contributed by Anthony Hart, 1-Sep-2011.)
Assertion
Ref Expression
nabi2  |-  ( (
ph 
<->  ps )  ->  (
( ch  -/\  ph )  <->  ( ch  -/\  ps )
) )

Proof of Theorem nabi2
StepHypRef Expression
1 anbi2 688 . . 3  |-  ( (
ph 
<->  ps )  ->  (
( ch  /\  ph ) 
<->  ( ch  /\  ps ) ) )
21notbid 285 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ( ch  /\  ph ) 
<->  -.  ( ch  /\  ps ) ) )
3 df-nan 1288 . 2  |-  ( ( ch  -/\  ph )  <->  -.  ( ch  /\  ph ) )
4 df-nan 1288 . 2  |-  ( ( ch  -/\  ps )  <->  -.  ( ch  /\  ps ) )
52, 3, 43bitr4g 279 1  |-  ( (
ph 
<->  ps )  ->  (
( ch  -/\  ph )  <->  ( ch  -/\  ps )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358    -/\ wnan 1287
This theorem is referenced by:  nabi2i  24903
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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