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Mirrors > Home > MPE Home > Th. List > simp3r2 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3r2 | ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr2 1194 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓) | |
2 | 1 | 3ad2ant3 1134 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1086 |
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 396 df-3an 1088 |
This theorem is referenced by: nllyrest 23311 cdlemblem 39131 cdleme21 39675 cdleme22b 39679 cdleme40m 39805 cdlemg34 40050 cdlemk5u 40199 cdlemk6u 40200 cdlemk21N 40211 cdlemk20 40212 cdlemk26b-3 40243 cdlemk26-3 40244 cdlemk28-3 40246 cdlemky 40264 cdlemk11t 40284 cdlemkyyN 40300 stoweidlem56 45234 |
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