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Theorem dfbi1 774
Description: Relate the biconditional connective to primitive connectives. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 31-Jan-2015.)
Assertion
Ref Expression
dfbi1 ((φψ) ↔ ¬ ((φψ) → ¬ (ψφ)))

Proof of Theorem dfbi1
StepHypRef Expression
1 dfbi2 366 . 2 ((φψ) ↔ ((φψ) (ψφ)))
2 df-an 771 . 2 (((φψ) (ψφ)) ↔ ¬ ((φψ) → ¬ (ψφ)))
31, 2bitri 172 1 ((φψ) ↔ ¬ ((φψ) → ¬ (ψφ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 96  wb 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100  ax-in1 526  ax-in2 527
This theorem depends on definitions:  df-bi 109
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