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Mirrors > Home > MPE Home > Th. List > simp1l2 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp1l2 | ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl2 1058 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓) | |
2 | 1 | 3ad2ant1 1075 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
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 196 df-an 385 df-3an 1033 |
This theorem is referenced by: mapxpen 8011 lsmcv 18962 pmatcollpw2 20402 btwnconn1lem4 31367 linethru 31430 hlrelat3 33716 cvrval3 33717 cvrval4N 33718 2atlt 33743 atbtwnex 33752 1cvratlt 33778 atcvrlln2 33823 atcvrlln 33824 2llnmat 33828 lvolnlelpln 33889 lnjatN 34084 lncmp 34087 cdlemd9 34511 dihord5b 35566 dihmeetALTN 35634 mapdrvallem2 35952 |
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