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Theorem pm3.48 775
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.) (Revised by NM, 1-Dec-2012.)
Assertion
Ref Expression
pm3.48 (((𝜑𝜓) ∧ (𝜒𝜃)) → ((𝜑𝜒) → (𝜓𝜃)))

Proof of Theorem pm3.48
StepHypRef Expression
1 orc 702 . . 3 (𝜓 → (𝜓𝜃))
21imim2i 12 . 2 ((𝜑𝜓) → (𝜑 → (𝜓𝜃)))
3 olc 701 . . 3 (𝜃 → (𝜓𝜃))
43imim2i 12 . 2 ((𝜒𝜃) → (𝜒 → (𝜓𝜃)))
52, 4jaao 709 1 (((𝜑𝜓) ∧ (𝜒𝜃)) → ((𝜑𝜒) → (𝜓𝜃)))
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:  orim12d  776
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