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| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) | 
| Ref | Expression | 
|---|---|
| simp3l3 | ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | simpl3 1194 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) | |
| 2 | 1 | 3ad2ant3 1136 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 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: cvmlift2lem10 35317 cdleme36m 40463 cdlemk5u 40863 cdlemk21N 40875 cdlemk20 40876 cdlemk27-3 40909 cdlemk28-3 40910 dihmeetlem20N 41328 | 
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