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Mirrors > Home > MPE Home > Th. List > simp322 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp322 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp22 1088 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant3 1077 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1031 |
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 196 df-an 385 df-3an 1033 |
This theorem is referenced by: dalemqnet 33956 dalemrot 33961 dath2 34041 cdleme18d 34600 cdleme20i 34623 cdleme20j 34624 cdleme20l2 34627 cdleme20l 34628 cdleme20m 34629 cdleme20 34630 cdleme21j 34642 cdleme22eALTN 34651 cdleme26eALTN 34667 cdlemk16a 35162 cdlemk12u-2N 35196 cdlemk21-2N 35197 cdlemk22 35199 cdlemk31 35202 cdlemk32 35203 cdlemk11ta 35235 cdlemk11tc 35251 |
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