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| Mirrors > Home > MPE Home > Th. List > simp312 | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
| Ref | Expression |
|---|---|
| simp312 | ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simp12 1205 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
| 2 | 1 | 3ad2ant3 1136 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∧ 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: dalemrot 39659 dalem-cly 39673 dath2 39739 cdleme26e 40361 cdleme38m 40465 cdleme38n 40466 cdleme39n 40468 cdlemg28b 40705 cdlemk7 40850 cdlemk11 40851 cdlemk12 40852 cdlemk7u 40872 cdlemk11u 40873 cdlemk12u 40874 cdlemk22 40895 cdlemk23-3 40904 cdlemk25-3 40906 |
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