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Theorem dfbi2 609
Description: A theorem similar to the standard definition of the biconditional. Definition of [Margaris] p. 49. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
dfbi2  |-  ( (
ph 
<->  ps )  <->  ( ( ph  ->  ps )  /\  ( ps  ->  ph )
) )

Proof of Theorem dfbi2
StepHypRef Expression
1 dfbi1 184 . 2  |-  ( (
ph 
<->  ps )  <->  -.  (
( ph  ->  ps )  ->  -.  ( ps  ->  ph ) ) )
2 df-an 360 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  <->  -.  (
( ph  ->  ps )  ->  -.  ( ps  ->  ph ) ) )
31, 2bitr4i 243 1  |-  ( (
ph 
<->  ps )  <->  ( ( ph  ->  ps )  /\  ( ps  ->  ph )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  dfbi  610  pm4.71  611  pm5.17  858  xor  861  albiim  1600  nfbi  1774  sbbi  2013  cleqh  2382  ralbiim  2682  reu8  2963  sseq2  3202  soeq2  4336  fun11  5317  dffo3  5677  isnsg2  14649  axextprim  24049  biimpexp  24072  axextndbi  24163  aibandbiaiffaiffb  27873  aibandbiaiaiffb  27874  aibnbna  27885
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
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