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Theorem dfbi2 612
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 186 . 2  |-  ( (
ph 
<->  ps )  <->  -.  (
( ph  ->  ps )  ->  -.  ( ps  ->  ph ) ) )
2 df-an 362 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  <->  -.  (
( ph  ->  ps )  ->  -.  ( ps  ->  ph ) ) )
31, 2bitr4i 245 1  |-  ( (
ph 
<->  ps )  <->  ( ( ph  ->  ps )  /\  ( ps  ->  ph )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178    /\ wa 360
This theorem is referenced by:  dfbi  613  pm4.71  614  pm5.17  863  xor  866  albiim  1612  nfbi  1738  sbbi  1963  cleqh  2346  ralbiim  2642  reu8  2900  sseq2  3121  soeq2  4227  fun11  5172  dffo3  5527  isnsg2  14482  axextprim  23218  biimpexp  23241  axextndbi  23329  equextvK  27874
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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