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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 1191 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) | |
2 | 1 | 3ad2ant1 1131 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1085 |
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 206 df-an 396 df-3an 1087 |
This theorem is referenced by: poxp3 8149 btwnconn1lem7 35683 btwnconn1lem12 35688 linethru 35743 hlrelat3 38879 cvrval3 38880 2atlt 38906 atbtwnex 38915 1cvratlt 38941 2llnmat 38991 lplnexllnN 39031 4atlem11 39076 lnjatN 39247 lncvrat 39249 lncmp 39250 cdlemd9 39673 dihord5b 40726 dihmeetALTN 40794 dih1dimatlem0 40795 mapdrvallem2 41112 grumnudlem 43716 itsclc0yqsol 47831 itschlc0xyqsol 47834 |
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