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Theorem bj-dfbi4 30934
Description: Alternate definition of the biconditional. (Contributed by BJ, 4-Oct-2019.)
Assertion
Ref Expression
bj-dfbi4  |-  ( (
ph 
<->  ps )  <->  ( ( ph  /\  ps )  \/ 
-.  ( ph  \/  ps ) ) )

Proof of Theorem bj-dfbi4
StepHypRef Expression
1 dfbi3 901 . 2  |-  ( (
ph 
<->  ps )  <->  ( ( ph  /\  ps )  \/  ( -.  ph  /\  -.  ps ) ) )
2 pm4.56 497 . . 3  |-  ( ( -.  ph  /\  -.  ps ) 
<->  -.  ( ph  \/  ps ) )
32orbi2i 521 . 2  |-  ( ( ( ph  /\  ps )  \/  ( -.  ph 
/\  -.  ps )
)  <->  ( ( ph  /\ 
ps )  \/  -.  ( ph  \/  ps )
) )
41, 3bitri 252 1  |-  ( (
ph 
<->  ps )  <->  ( ( ph  /\  ps )  \/ 
-.  ( ph  \/  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ wo 369    /\ wa 370
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-or 371  df-an 372
This theorem is referenced by:  bj-dfbi5  30935
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