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Mirrors > Home > MPE Home > Th. List > Mathboxes > rp-simp2-frege | Structured version Visualization version GIF version |
Description: Simplification of triple conjunction. Compare with simp2 1136. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
rp-simp2-frege | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege1 41368 | . 2 ⊢ (𝜓 → (𝜒 → 𝜓)) | |
2 | ax-frege1 41368 | . 2 ⊢ ((𝜓 → (𝜒 → 𝜓)) → (𝜑 → (𝜓 → (𝜒 → 𝜓)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 41368 |
This theorem is referenced by: rp-simp2 41371 rp-frege24 41375 rp-4frege 41380 |
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