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| Mirrors > Home > MPE Home > Th. List > simp3r3 | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
| Ref | Expression |
|---|---|
| simp3r3 | ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpr3 1197 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒) | |
| 2 | 1 | 3ad2ant3 1136 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 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: hash7g 14525 nllyrest 23494 cdlemblem 39795 cdleme21 40339 cdleme22b 40343 cdleme40m 40469 cdlemg34 40714 cdlemk5u 40863 cdlemk6u 40864 cdlemk21N 40875 cdlemk20 40876 cdlemk26b-3 40907 cdlemk26-3 40908 cdlemk28-3 40910 cdlemky 40928 cdlemk11t 40948 cdlemkyyN 40964 dihmeetlem20N 41328 stoweidlem56 46071 |
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