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Theorem dfbi2 365
 Description: A theorem similar to the standard definition of the biconditional. Definition of [Margaris] p. 49. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 31-Jan-2015.)
Assertion
Ref Expression
dfbi2 ((φψ) ↔ ((φψ) (ψφ)))

Proof of Theorem dfbi2
StepHypRef Expression
1 df-bi 108 . . 3 (((φψ) → ((φψ) (ψφ))) (((φψ) (ψφ)) → (φψ)))
21simpli 102 . 2 ((φψ) → ((φψ) (ψφ)))
31simpri 104 . 2 (((φψ) (ψφ)) → (φψ))
42, 3impbii 115 1 ((φψ) ↔ ((φψ) (ψφ)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 95   ↔ wb 96 This theorem is referenced by:  pm4.71  366  dfbi1  775  pm5.17  799  dcbi  821  orbididc  837  trubifal  1239  albiim  1308  hbbi  1371  hbbid  1396  a4sbbi  1600  sbbi  1698  xor  1899 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99 This theorem depends on definitions:  df-bi 108
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