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Theorem dfbi2 366
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 109 . . 3 (((φψ) → ((φψ) (ψφ))) (((φψ) (ψφ)) → (φψ)))
21simpli 103 . 2 ((φψ) → ((φψ) (ψφ)))
31simpri 105 . 2 (((φψ) (ψφ)) → (φψ))
42, 3impbii 116 1 ((φψ) ↔ ((φψ) (ψφ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 96  wb 97
This theorem is referenced by:  pm4.71  367  dfbi1  774  pm5.17  815  xor  818  albiim  1285  hbbi  1342  hbbid  1366  sbbi  1552
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100
This theorem depends on definitions:  df-bi 109
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