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Theorem pm3.44 534
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 id 22 . 2 ((𝜓𝜑) → (𝜓𝜑))
2 id 22 . 2 ((𝜒𝜑) → (𝜒𝜑))
31, 2jaao 532 1 (((𝜓𝜑) ∧ (𝜒𝜑)) → ((𝜓𝜒) → 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382  wa 383
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-or 384  df-an 385
This theorem is referenced by:  jao  535  jaob  857  dvmptconst  40549  dvmptidg  40551  dvmulcncf  40560  dvdivcncf  40562  fourierdlem101  40844
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