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Theorem pm5.1 830
Description: Two propositions are equivalent if they are both true. Theorem *5.1 of [WhiteheadRussell] p. 123. (Contributed by NM, 21-May-1994.)
Assertion
Ref Expression
pm5.1 ((φ ψ) → (φψ))

Proof of Theorem pm5.1
StepHypRef Expression
1 pm5.501 330 . 2 (φ → (ψ ↔ (φψ)))
21biimpa 470 1 ((φ ψ) → (φψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  pm5.35  869  ssconb  3399  raaan  3657  raaanv  3658
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