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Mirrors > Home > NFE Home > Th. List > orim12d | GIF version |
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 10-May-1994.) |
Ref | Expression |
---|---|
orim12d.1 | ⊢ (φ → (ψ → χ)) |
orim12d.2 | ⊢ (φ → (θ → τ)) |
Ref | Expression |
---|---|
orim12d | ⊢ (φ → ((ψ ∨ θ) → (χ ∨ τ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orim12d.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | orim12d.2 | . 2 ⊢ (φ → (θ → τ)) | |
3 | pm3.48 806 | . 2 ⊢ (((ψ → χ) ∧ (θ → τ)) → ((ψ ∨ θ) → (χ ∨ τ))) | |
4 | 1, 2, 3 | syl2anc 642 | 1 ⊢ (φ → ((ψ ∨ θ) → (χ ∨ τ))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 357 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 |
This theorem is referenced by: orim1d 812 orim2d 813 3orim123d 1260 preq12b 4127 evenoddnnnul 4514 funun 5146 enprmaplem3 6078 leconnnc 6218 nchoicelem9 6297 nchoicelem17 6305 |
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