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Mirrors > Home > MPE Home > Th. List > simp1l3 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp1l3 | ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl3 1231 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) | |
2 | 1 | 3ad2ant1 1127 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 382 ∧ w3a 1071 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 383 df-3an 1073 |
This theorem is referenced by: btwnconn1lem7 32530 btwnconn1lem12 32535 linethru 32590 hlrelat3 35213 cvrval3 35214 2atlt 35240 atbtwnex 35249 1cvratlt 35275 2llnmat 35325 lplnexllnN 35365 4atlem11 35410 lnjatN 35581 lncvrat 35583 lncmp 35584 cdlemd9 36008 dihord5b 37062 dihmeetALTN 37130 dih1dimatlem0 37131 mapdrvallem2 37448 |
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