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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 1202 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1083 |
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 209 df-an 399 df-3an 1085 |
This theorem is referenced by: dalemcnes 36788 dalempnes 36789 dalemrot 36795 dath2 36875 cdleme18d 37433 cdleme20i 37455 cdleme20j 37456 cdleme20l2 37459 cdleme20l 37460 cdleme20m 37461 cdleme20 37462 cdleme21j 37474 cdleme22eALTN 37483 cdlemk16a 37994 cdlemk12u-2N 38028 cdlemk21-2N 38029 cdlemk22 38031 cdlemk31 38034 cdlemk32 38035 cdlemk11ta 38067 cdlemk11tc 38083 |
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