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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nnclavi | Structured version Visualization version GIF version |
Description: Inference associated with bj-nnclav 34463. Its associated inference is an instance of syl 17. Notice the non-intuitionistic proof from bj-peircei 34483 and bj-poni 34462. (Contributed by BJ, 30-Jul-2024.) |
Ref | Expression |
---|---|
bj-nnclavi.1 | ⊢ ((𝜑 → 𝜓) → 𝜑) |
Ref | Expression |
---|---|
bj-nnclavi | ⊢ ((𝜑 → 𝜓) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnclavi.1 | . 2 ⊢ ((𝜑 → 𝜓) → 𝜑) | |
2 | bj-nnclav 34463 | . 2 ⊢ (((𝜑 → 𝜓) → 𝜑) → ((𝜑 → 𝜓) → 𝜓)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → 𝜓) → 𝜓) |
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: (None) |
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