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Mirrors > Home > NFE Home > Th. List > expimpd | GIF version |
Description: Exportation followed by a deduction version of importation. (Contributed by NM, 6-Sep-2008.) |
Ref | Expression |
---|---|
expimpd.1 | ⊢ ((φ ∧ ψ) → (χ → θ)) |
Ref | Expression |
---|---|
expimpd | ⊢ (φ → ((ψ ∧ χ) → θ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | expimpd.1 | . . 3 ⊢ ((φ ∧ ψ) → (χ → θ)) | |
2 | 1 | ex 423 | . 2 ⊢ (φ → (ψ → (χ → θ))) |
3 | 2 | imp3a 420 | 1 ⊢ (φ → ((ψ ∧ χ) → θ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 |
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-an 360 |
This theorem is referenced by: tfindi 4496 elpreima 5407 enmap2lem3 6065 enmap1lem3 6071 ncdisjun 6136 ncssfin 6151 leltctr 6212 letc 6231 nchoicelem8 6296 nchoicelem12 6300 |
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