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Mirrors > Home > MPE Home > Th. List > Mathboxes > rp-6frege | Structured version Visualization version GIF version |
Description: Elimination of a nested antecedent of special form. (Contributed by RP, 24-Dec-2019.) |
Ref | Expression |
---|---|
rp-6frege | ⊢ (𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rp-4frege 40956 | . 2 ⊢ ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃)) | |
2 | ax-frege1 40944 | . 2 ⊢ (((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃)) → (𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 40944 ax-frege2 40945 |
This theorem is referenced by: rp-8frege 40958 |
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