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Mirrors > Home > MPE Home > Th. List > simp113 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp113 | ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp13 1202 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒) | |
2 | 1 | 3ad2ant1 1130 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1084 |
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 395 df-3an 1086 |
This theorem is referenced by: axcontlem4 28901 llncvrlpln2 39256 4atlem12b 39310 2lnat 39483 cdlemblem 39492 4atexlemex6 39773 cdleme24 40051 cdleme26ee 40059 cdlemg2idN 40295 dihglblem2N 40993 0ellimcdiv 45270 limclner 45272 |
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