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Mirrors > Home > NFE Home > Th. List > olcd | GIF version |
Description: Deduction introducing a disjunct. A translation of natural deduction rule ∨ IL ( ∨ insertion left), see natded in set.mm. (Contributed by NM, 11-Apr-2008.) (Proof shortened by Wolf Lammen, 3-Oct-2013.) |
Ref | Expression |
---|---|
orcd.1 | ⊢ (φ → ψ) |
Ref | Expression |
---|---|
olcd | ⊢ (φ → (χ ∨ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcd.1 | . . 3 ⊢ (φ → ψ) | |
2 | 1 | orcd 381 | . 2 ⊢ (φ → (ψ ∨ χ)) |
3 | 2 | orcomd 377 | 1 ⊢ (φ → (χ ∨ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 357 |
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 177 df-or 359 |
This theorem is referenced by: pm2.48 389 pm2.49 390 orim12i 502 pm1.5 508 nnc0suc 4412 clos1basesuc 5882 nc0le1 6216 frecsuc 6322 |
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