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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 1196 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant2 1126 | 1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1079 |
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 208 df-an 397 df-3an 1081 |
This theorem is referenced by: cdleme27a 37383 cdlemk5u 37877 cdlemk6u 37878 cdlemk7u 37886 cdlemk11u 37887 cdlemk12u 37888 cdlemk7u-2N 37904 cdlemk11u-2N 37905 cdlemk12u-2N 37906 cdlemk20-2N 37908 cdlemk22 37909 cdlemk22-3 37917 cdlemk33N 37925 cdlemk53b 37972 cdlemk53 37973 cdlemk55a 37975 cdlemkyyN 37978 cdlemk43N 37979 |
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