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| Mirrors > Home > MPE Home > Th. List > simp322 | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
| Ref | Expression |
|---|---|
| simp322 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simp22 1208 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓) | |
| 2 | 1 | 3ad2ant3 1136 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 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: dalemqnet 39654 dalemrot 39659 dath2 39739 cdleme18d 40297 cdleme20i 40319 cdleme20j 40320 cdleme20l2 40323 cdleme20l 40324 cdleme20m 40325 cdleme20 40326 cdleme21j 40338 cdleme22eALTN 40347 cdleme26eALTN 40363 cdlemk16a 40858 cdlemk12u-2N 40892 cdlemk21-2N 40893 cdlemk22 40895 cdlemk31 40898 cdlemk32 40899 cdlemk11ta 40931 cdlemk11tc 40947 |
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