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Mirrors > Home > MPE Home > Th. List > simp323 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp323 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp23 1200 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒) | |
2 | 1 | 3ad2ant3 1127 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1079 |
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 208 df-an 397 df-3an 1081 |
This theorem is referenced by: dalemrot 36673 dath2 36753 cdleme18d 37311 cdleme20i 37333 cdleme20j 37334 cdleme20l2 37337 cdleme20l 37338 cdleme20m 37339 cdleme20 37340 cdleme21j 37352 cdleme22eALTN 37361 cdleme26eALTN 37377 cdlemk16a 37872 cdlemk12u-2N 37906 cdlemk21-2N 37907 cdlemk22 37909 cdlemk31 37912 cdlemk11ta 37945 |
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