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Mirrors > Home > MPE Home > Th. List > simp212 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp212 | ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp12 1218 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant2 1125 | 1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1071 |
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 387 df-3an 1073 |
This theorem is referenced by: cdleme27a 36521 cdlemk5u 37015 cdlemk6u 37016 cdlemk7u 37024 cdlemk11u 37025 cdlemk12u 37026 cdlemk7u-2N 37042 cdlemk11u-2N 37043 cdlemk12u-2N 37044 cdlemk20-2N 37046 cdlemk22 37047 cdlemk22-3 37055 cdlemk33N 37063 cdlemk53b 37110 cdlemk53 37111 cdlemk55a 37113 cdlemkyyN 37116 cdlemk43N 37117 |
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