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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 1203 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant3 1132 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1084 |
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 210 df-an 400 df-3an 1086 |
This theorem is referenced by: dalemcnes 36946 dalempnes 36947 dalemrot 36953 dath2 37033 cdleme18d 37591 cdleme20i 37613 cdleme20j 37614 cdleme20l2 37617 cdleme20l 37618 cdleme20m 37619 cdleme20 37620 cdleme21j 37632 cdleme22eALTN 37641 cdlemk16a 38152 cdlemk12u-2N 38186 cdlemk21-2N 38187 cdlemk22 38189 cdlemk31 38192 cdlemk32 38193 cdlemk11ta 38225 cdlemk11tc 38241 |
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