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Theorem bi3 117
Description: Property of the biconditional connective. (Contributed by NM, 11-May-1999.)
Assertion
Ref Expression
bi3 ((𝜑𝜓) → ((𝜓𝜑) → (𝜑𝜓)))

Proof of Theorem bi3
StepHypRef Expression
1 df-bi 115 . . 3 (((𝜑𝜓) → ((𝜑𝜓) ∧ (𝜓𝜑))) ∧ (((𝜑𝜓) ∧ (𝜓𝜑)) → (𝜑𝜓)))
21simpri 111 . 2 (((𝜑𝜓) ∧ (𝜓𝜑)) → (𝜑𝜓))
32ex 113 1 ((𝜑𝜓) → ((𝜓𝜑) → (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  impbii  124  impbidd  125  bisym  223  bezoutlembi  10788
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