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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 1088 |
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 210 df-an 400 df-3an 1090 |
This theorem is referenced by: axcontlem4 26905 ps-2b 37108 llncvrlpln2 37183 4atlem11b 37234 4atlem12b 37237 2lnat 37410 cdlemblem 37419 4atexlemex6 37700 cdleme24 37978 cdleme26ee 37986 cdlemg2idN 38222 cdlemg31c 38325 cdlemk26-3 38532 dihglblem2N 38920 0ellimcdiv 42716 |
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