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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 954 | 1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 ∨ 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 206 df-an 398 df-or 847 |
This theorem is referenced by: jao 960 jaob 961 ssfi 9124 dvmptconst 44230 dvmptidg 44232 dvmulcncf 44240 dvdivcncf 44242 fourierdlem101 44522 |
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