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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 1206 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant3 1135 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1087 |
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 206 df-an 397 df-3an 1089 |
This theorem is referenced by: dalemcnes 38324 dalempnes 38325 dalemrot 38331 dath2 38411 cdleme18d 38969 cdleme20i 38991 cdleme20j 38992 cdleme20l2 38995 cdleme20l 38996 cdleme20m 38997 cdleme20 38998 cdleme21j 39010 cdleme22eALTN 39019 cdlemk16a 39530 cdlemk12u-2N 39564 cdlemk21-2N 39565 cdlemk22 39567 cdlemk31 39570 cdlemk32 39571 cdlemk11ta 39603 cdlemk11tc 39619 |
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