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Mirrors > Home > MPE Home > Th. List > olcs | Structured version Visualization version GIF version |
Description: Deduction eliminating disjunct. (Contributed by NM, 21-Jun-1994.) (Proof shortened by Wolf Lammen, 3-Oct-2013.) |
Ref | Expression |
---|---|
olcs.1 | ⊢ ((𝜑 ∨ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
olcs | ⊢ (𝜓 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olcs.1 | . . 3 ⊢ ((𝜑 ∨ 𝜓) → 𝜒) | |
2 | 1 | orcoms 403 | . 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜒) |
3 | 2 | orcs 408 | 1 ⊢ (𝜓 → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 382 |
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 196 df-or 384 |
This theorem is referenced by: 0nn0 11184 fsum00 14371 pcfac 15441 mndifsplit 20261 bposlem2 24810 axcgrid 25596 3o2cs 28694 3o3cs 28695 finxpreclem2 32403 itg2addnclem 32631 tsan3 33120 |
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