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Mirrors > Home > MPE Home > Th. List > simp321 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp321 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp21 1249 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant3 1130 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1072 |
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 197 df-an 385 df-3an 1074 |
This theorem is referenced by: dalemcnes 35457 dalempnes 35458 dalemrot 35464 dath2 35544 cdleme18d 36103 cdleme20i 36125 cdleme20j 36126 cdleme20l2 36129 cdleme20l 36130 cdleme20m 36131 cdleme20 36132 cdleme21j 36144 cdleme22eALTN 36153 cdlemk16a 36664 cdlemk12u-2N 36698 cdlemk21-2N 36699 cdlemk22 36701 cdlemk31 36704 cdlemk32 36705 cdlemk11ta 36737 cdlemk11tc 36753 |
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