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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 1092 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant1 1082 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1037 |
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 197 df-an 386 df-3an 1039 |
This theorem is referenced by: axcontlem4 25847 ps-2b 34768 llncvrlpln2 34843 4atlem11b 34894 4atlem12b 34897 2lnat 35070 cdlemblem 35079 4atexlemex6 35360 cdleme24 35640 cdleme26ee 35648 cdlemg2idN 35884 cdlemg31c 35987 cdlemk26-3 36194 dihglblem2N 36583 0ellimcdiv 39881 |
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