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Mirrors > Home > MPE Home > Th. List > simp313 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp313 | ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp13 1201 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1083 |
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 209 df-an 399 df-3an 1085 |
This theorem is referenced by: dalemrot 36787 dalem5 36797 dalem-cly 36801 dath2 36867 cdleme26e 37489 cdleme38m 37593 cdleme38n 37594 cdlemg28b 37833 cdlemg28 37834 cdlemk7 37978 cdlemk11 37979 cdlemk12 37980 cdlemk7u 38000 cdlemk11u 38001 cdlemk12u 38002 cdlemk22 38023 cdlemk23-3 38032 cdlemk25-3 38034 |
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