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Mirrors > Home > MPE Home > Th. List > pm3.48 | Structured version Visualization version GIF version |
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.) |
Ref | Expression |
---|---|
pm3.48 | ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 866 | . . 3 ⊢ (𝜓 → (𝜓 ∨ 𝜃)) | |
2 | 1 | imim2i 16 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∨ 𝜃))) |
3 | olc 867 | . . 3 ⊢ (𝜃 → (𝜓 ∨ 𝜃)) | |
4 | 3 | imim2i 16 | . 2 ⊢ ((𝜒 → 𝜃) → (𝜒 → (𝜓 ∨ 𝜃))) |
5 | 2, 4 | jaao 954 | 1 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∨ wo 846 |
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 210 df-an 400 df-or 847 |
This theorem is referenced by: orim12d 964 tz7.48lem 8099 caubnd 14801 bj-nnfor 34559 |
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