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Mirrors > Home > MPE Home > Th. List > simp311 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp311 | ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp11 1261 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant3 1166 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑) |
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: dalem-clpjq 35658 dath2 35758 cdleme26e 36380 cdleme38m 36484 cdleme38n 36485 cdleme39n 36487 cdlemg28b 36724 cdlemk7 36869 cdlemk11 36870 cdlemk12 36871 cdlemk7u 36891 cdlemk11u 36892 cdlemk12u 36893 cdlemk22 36914 cdlemk23-3 36923 cdlemk25-3 36925 |
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