| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| 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 1194 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) | |
| 2 | 1 | 3ad2ant1 1134 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1087 |
| 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 207 df-an 396 df-3an 1089 |
| This theorem is referenced by: poxp3 8175 btwnconn1lem7 36094 btwnconn1lem12 36099 linethru 36154 hlrelat3 39414 cvrval3 39415 2atlt 39441 atbtwnex 39450 1cvratlt 39476 2llnmat 39526 lplnexllnN 39566 4atlem11 39611 lnjatN 39782 lncvrat 39784 lncmp 39785 cdlemd9 40208 dihord5b 41261 dihmeetALTN 41329 dih1dimatlem0 41330 mapdrvallem2 41647 grumnudlem 44304 itsclc0yqsol 48685 itschlc0xyqsol 48688 |
| Copyright terms: Public domain | W3C validator |