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Mirrors > Home > ILE Home > Th. List > pm3.44 | 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 | jaob 700 | . 2 ⊢ (((𝜓 ∨ 𝜒) → 𝜑) ↔ ((𝜓 → 𝜑) ∧ (𝜒 → 𝜑))) | |
2 | 1 | biimpri 132 | 1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑)) |
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: jaoi 706 jao 745 pm2.6dc 848 pm4.83dc 936 |
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