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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 1192 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) | |
2 | 1 | 3ad2ant1 1132 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1086 |
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 1088 |
This theorem is referenced by: poxp3 8174 btwnconn1lem7 36075 btwnconn1lem12 36080 linethru 36135 hlrelat3 39395 cvrval3 39396 2atlt 39422 atbtwnex 39431 1cvratlt 39457 2llnmat 39507 lplnexllnN 39547 4atlem11 39592 lnjatN 39763 lncvrat 39765 lncmp 39766 cdlemd9 40189 dihord5b 41242 dihmeetALTN 41310 dih1dimatlem0 41311 mapdrvallem2 41628 grumnudlem 44281 itsclc0yqsol 48614 itschlc0xyqsol 48617 |
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