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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 1263 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒) | |
2 | 1 | 3ad2ant1 1164 | 1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1108 |
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 199 df-an 386 df-3an 1110 |
This theorem is referenced by: axcontlem4 26203 llncvrlpln2 35577 4atlem12b 35631 2lnat 35804 cdlemblem 35813 4atexlemex6 36094 cdleme24 36372 cdleme26ee 36380 cdlemg2idN 36616 dihglblem2N 37314 0ellimcdiv 40620 limclner 40622 |
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