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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nnclavc | Structured version Visualization version GIF version |
Description: Commuted form of bj-nnclav 34463. Notice the non-intuitionistic proof from bj-peircei 34483 and imim1i 63. (Contributed by BJ, 30-Jul-2024.) A proof which is shorter when compressed uses embantd 59. (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nnclavc | ⊢ ((𝜑 → 𝜓) → (((𝜑 → 𝜓) → 𝜑) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnclav 34463 | . 2 ⊢ (((𝜑 → 𝜓) → 𝜑) → ((𝜑 → 𝜓) → 𝜓)) | |
2 | 1 | com12 32 | 1 ⊢ ((𝜑 → 𝜓) → (((𝜑 → 𝜓) → 𝜑) → 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: bj-nnclavci 34466 |
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