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Mirrors > Home > MPE Home > Th. List > Mathboxes > rp-simp2 | Structured version Visualization version GIF version |
Description: Simplification of triple conjunction. Identical to simp2 1135. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
rp-simp2 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rp-simp2-frege 41289 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓))) | |
2 | 1 | 3imp 1109 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1085 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-frege1 41287 |
This theorem depends on definitions: df-bi 206 df-an 396 df-3an 1087 |
This theorem is referenced by: ntrclsk3 41569 |
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