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Mirrors > Home > MPE Home > Th. List > jao | Structured version Visualization version GIF version |
Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.) |
Ref | Expression |
---|---|
jao | ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((𝜑 ∨ 𝜒) → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.44 942 | . 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)) → ((𝜑 ∨ 𝜒) → 𝜓)) | |
2 | 1 | ex 405 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((𝜑 ∨ 𝜒) → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 833 |
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 199 df-an 388 df-or 834 |
This theorem is referenced by: 3jao 1405 en3lplem2 8870 indpi 10127 bj-orim2 33414 jaodd 38550 jaoded 40325 suctrALT2VD 40595 suctrALT2 40596 en3lplem2VD 40603 hbimpgVD 40663 ax6e2ndeqVD 40668 suctrALTcf 40681 suctrALTcfVD 40682 ax6e2ndeqALT 40690 |
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