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Theorem pm3.48 873
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.)
Assertion
Ref Expression
pm3.48 (((𝜑𝜓) ∧ (𝜒𝜃)) → ((𝜑𝜒) → (𝜓𝜃)))

Proof of Theorem pm3.48
StepHypRef Expression
1 orc 398 . . 3 (𝜓 → (𝜓𝜃))
21imim2i 16 . 2 ((𝜑𝜓) → (𝜑 → (𝜓𝜃)))
3 olc 397 . . 3 (𝜃 → (𝜓𝜃))
43imim2i 16 . 2 ((𝜒𝜃) → (𝜒 → (𝜓𝜃)))
52, 4jaao 529 1 (((𝜑𝜓) ∧ (𝜒𝜃)) → ((𝜑𝜒) → (𝜓𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381  wa 382
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 195  df-or 383  df-an 384
This theorem is referenced by:  orim12d  878  tz7.48lem  7400  caubnd  13892
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