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Theorem ibib 331
Description: Implication in terms of implication and biconditional. (Contributed by NM, 31-Mar-1994.) (Proof shortened by Wolf Lammen, 24-Jan-2013.)
Assertion
Ref Expression
ibib ((φψ) ↔ (φ → (φψ)))

Proof of Theorem ibib
StepHypRef Expression
1 pm5.501 330 . 2 (φ → (ψ ↔ (φψ)))
21pm5.74i 236 1 ((φψ) ↔ (φ → (φψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
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
This theorem is referenced by: (None)
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