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Mirrors > Home > MPE Home > Th. List > imim3i | Structured version Visualization version GIF version |
Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006.) |
Ref | Expression |
---|---|
imim3i.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
imim3i | ⊢ ((𝜃 → 𝜑) → ((𝜃 → 𝜓) → (𝜃 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim3i.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | imim2i 16 | . 2 ⊢ ((𝜃 → 𝜑) → (𝜃 → (𝜓 → 𝜒))) |
3 | 2 | a2d 29 | 1 ⊢ ((𝜃 → 𝜑) → ((𝜃 → 𝜓) → (𝜃 → 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: pm2.83 84 pm5.74 269 pm3.43i 473 sbi1 2074 ral2imi 3082 ceqsalt 3462 elabgt 3603 bj-bi3ant 34771 bj-ceqsalt0 35069 bj-ceqsalt1 35070 pm10.57 41989 ee33 42141 |
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