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| Mirrors > Home > MPE Home > Th. List > pm3.44 | Structured version Visualization version GIF version | ||
| Description: Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 3-Oct-2013.) |
| Ref | Expression |
|---|---|
| pm3.44 | ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ ((𝜓 → 𝜑) → (𝜓 → 𝜑)) | |
| 2 | id 22 | . 2 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜑)) | |
| 3 | 1, 2 | jaao 957 | 1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑)) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∧ wa 395 ∨ wo 848 |
| 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 207 df-an 396 df-or 849 |
| This theorem is referenced by: jao 963 jaob 964 ssfi 9213 dvmptconst 45930 dvmptidg 45932 dvmulcncf 45940 dvdivcncf 45942 fourierdlem101 46222 |
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