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Mirrors > Home > NFE Home > Th. List > exp42 | GIF version |
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
exp42.1 | ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ) |
Ref | Expression |
---|---|
exp42 | ⊢ (φ → (ψ → (χ → (θ → τ)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp42.1 | . . 3 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ) | |
2 | 1 | exp31 587 | . 2 ⊢ (φ → ((ψ ∧ χ) → (θ → τ))) |
3 | 2 | exp3a 425 | 1 ⊢ (φ → (ψ → (χ → (θ → τ)))) |
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: f1o2d 5727 |
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