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| Mirrors > Home > MPE Home > Th. List > simp112 | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
| Ref | Expression |
|---|---|
| simp112 | ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simp12 1205 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
| 2 | 1 | 3ad2ant1 1134 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 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: axcontlem4 28982 ps-2b 39484 llncvrlpln2 39559 4atlem11b 39610 4atlem12b 39613 2lnat 39786 cdlemblem 39795 4atexlemex6 40076 cdleme24 40354 cdleme26ee 40362 cdlemg2idN 40598 cdlemg31c 40701 cdlemk26-3 40908 dihglblem2N 41296 0ellimcdiv 45664 |
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