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Mirrors > Home > ILE Home > Th. List > pm3.48 | GIF version |
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.) (Revised by NM, 1-Dec-2012.) |
Ref | Expression |
---|---|
pm3.48 | ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 633 | . . 3 ⊢ (𝜓 → (𝜓 ∨ 𝜃)) | |
2 | 1 | imim2i 12 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∨ 𝜃))) |
3 | olc 632 | . . 3 ⊢ (𝜃 → (𝜓 ∨ 𝜃)) | |
4 | 3 | imim2i 12 | . 2 ⊢ ((𝜒 → 𝜃) → (𝜒 → (𝜓 ∨ 𝜃))) |
5 | 2, 4 | jaao 639 | 1 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ∨ wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: orim12d 700 |
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