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Theorem dfbi 610
 Description: Definition df-bi 177 rewritten in an abbreviated form to help intuitive understanding of that definition. Note that it is a conjunction of two implications; one which asserts properties that follow from the biconditional and one which asserts properties that imply the biconditional. (Contributed by NM, 15-Aug-2008.)
Assertion
Ref Expression
dfbi (((φψ) → ((φψ) (ψφ))) (((φψ) (ψφ)) → (φψ)))

Proof of Theorem dfbi
StepHypRef Expression
1 dfbi2 609 . . 3 ((φψ) ↔ ((φψ) (ψφ)))
21biimpi 186 . 2 ((φψ) → ((φψ) (ψφ)))
31biimpri 197 . 2 (((φψ) (ψφ)) → (φψ))
42, 3pm3.2i 441 1 (((φψ) → ((φψ) (ψφ))) (((φψ) (ψφ)) → (φψ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by: (None)
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