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Mirrors > Home > NFE Home > Th. List > orim12i | GIF version |
Description: Disjoin antecedents and consequents of two premises. (Contributed by NM, 6-Jun-1994.) (Proof shortened by Wolf Lammen, 25-Jul-2012.) |
Ref | Expression |
---|---|
orim12i.1 | ⊢ (φ → ψ) |
orim12i.2 | ⊢ (χ → θ) |
Ref | Expression |
---|---|
orim12i | ⊢ ((φ ∨ χ) → (ψ ∨ θ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orim12i.1 | . . 3 ⊢ (φ → ψ) | |
2 | 1 | orcd 381 | . 2 ⊢ (φ → (ψ ∨ θ)) |
3 | orim12i.2 | . . 3 ⊢ (χ → θ) | |
4 | 3 | olcd 382 | . 2 ⊢ (χ → (ψ ∨ θ)) |
5 | 2, 4 | jaoi 368 | 1 ⊢ ((φ ∨ χ) → (ψ ∨ θ)) |
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: orim1i 503 orim2i 504 prlem2 929 eueq3 3011 lefinlteq 4463 funcnvuni 5161 muc0or 6252 nchoicelem9 6297 |
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