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Theorem pm4.42 1040
Description: Theorem *4.42 of [WhiteheadRussell] p. 119. See also ifpid 1062. (Contributed by Roy F. Longton, 21-Jun-2005.)
Assertion
Ref Expression
pm4.42 (𝜑 ↔ ((𝜑𝜓) ∨ (𝜑 ∧ ¬ 𝜓)))

Proof of Theorem pm4.42
StepHypRef Expression
1 dedlema 1030 . 2 (𝜓 → (𝜑 ↔ ((𝜑𝜓) ∨ (𝜑 ∧ ¬ 𝜓))))
2 dedlemb 1031 . 2 𝜓 → (𝜑 ↔ ((𝜑𝜓) ∨ (𝜑 ∧ ¬ 𝜓))))
31, 2pm2.61i 176 1 (𝜑 ↔ ((𝜑𝜓) ∨ (𝜑 ∧ ¬ 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 382  wo 834
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 197  df-an 383  df-or 835
This theorem is referenced by:  inundif  4188  numclwwlk3lemOLD  27580  elim2ifim  29702  smatrcl  30202  expdioph  38116
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