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Mirrors > Home > NFE Home > Th. List > expdimp | GIF version |
Description: A deduction version of exportation, followed by importation. (Contributed by NM, 6-Sep-2008.) |
Ref | Expression |
---|---|
exp3a.1 | ⊢ (φ → ((ψ ∧ χ) → θ)) |
Ref | Expression |
---|---|
expdimp | ⊢ ((φ ∧ ψ) → (χ → θ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp3a.1 | . . 3 ⊢ (φ → ((ψ ∧ χ) → θ)) | |
2 | 1 | exp3a 425 | . 2 ⊢ (φ → (ψ → (χ → θ))) |
3 | 2 | imp 418 | 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: rexlimdvv 2744 ralcom2 2775 reu6 3025 preaddccan2 4455 ltfinasym 4460 lenltfin 4469 vfinspsslem1 4550 phi11lem1 4595 fun11iun 5305 erth 5968 ltlenlec 6207 leltctr 6212 tlecg 6230 |
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