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Mirrors > Home > MPE Home > Th. List > simp1l1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp1l1 | ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl1 1188 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑) | |
2 | 1 | 3ad2ant1 1130 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 ∧ w3a 1084 |
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 395 df-3an 1086 |
This theorem is referenced by: poxp3 8155 mapxpen 9168 lsmcv 21041 sltlpss 27879 archiabl 32998 trisegint 35755 linethru 35880 hlrelat3 39015 cvrval3 39016 cvrval4N 39017 2atlt 39042 atbtwnex 39051 1cvratlt 39077 atcvrlln2 39122 atcvrlln 39123 2llnmat 39127 lplnexllnN 39167 lvolnlelpln 39188 lnjatN 39383 lncvrat 39385 lncmp 39386 cdlemd9 39809 dihord5b 40862 dihmeetALTN 40930 dih1dimatlem0 40931 mapdrvallem2 41248 grumnudlem 43864 |
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