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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 1084 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant3 1077 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1031 |
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 196 df-an 385 df-3an 1033 |
This theorem is referenced by: dalem-clpjq 33941 dath2 34041 cdleme26e 34665 cdleme38m 34769 cdleme38n 34770 cdleme39n 34772 cdlemg28b 35009 cdlemk7 35154 cdlemk11 35155 cdlemk12 35156 cdlemk7u 35176 cdlemk11u 35177 cdlemk12u 35178 cdlemk22 35199 cdlemk23-3 35208 cdlemk25-3 35210 |
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