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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 1085 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant2 1076 | 1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓) |
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: cdleme27a 34673 cdlemk5u 35167 cdlemk6u 35168 cdlemk7u 35176 cdlemk11u 35177 cdlemk12u 35178 cdlemk7u-2N 35194 cdlemk11u-2N 35195 cdlemk12u-2N 35196 cdlemk20-2N 35198 cdlemk22 35199 cdlemk22-3 35207 cdlemk33N 35215 cdlemk53b 35262 cdlemk53 35263 cdlemk55a 35265 cdlemkyyN 35268 cdlemk43N 35269 |
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