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Theorem pm3.44 705
Description: Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)
Assertion
Ref Expression
pm3.44 (((𝜓𝜑) ∧ (𝜒𝜑)) → ((𝜓𝜒) → 𝜑))

Proof of Theorem pm3.44
StepHypRef Expression
1 jaob 700 . 2 (((𝜓𝜒) → 𝜑) ↔ ((𝜓𝜑) ∧ (𝜒𝜑)))
21biimpri 132 1 (((𝜓𝜑) ∧ (𝜒𝜑)) → ((𝜓𝜒) → 𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wo 698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  jaoi  706  jao  745  pm2.6dc  848  pm4.83dc  936
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