Theorem simp321 1325

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp321	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Proof of Theorem simp321

Step	Hyp	Ref	Expression
1		simp21 1208	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1136	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  dalemcnes  40026  dalempnes  40027  dalemrot  40033  dath2  40113  cdleme18d  40671  cdleme20i  40693  cdleme20j  40694  cdleme20l2  40697  cdleme20l  40698  cdleme20m  40699  cdleme20  40700  cdleme21j  40712  cdleme22eALTN  40721  cdlemk16a  41232  cdlemk12u-2N  41266  cdlemk21-2N  41267  cdlemk22  41269  cdlemk31  41272  cdlemk32  41273  cdlemk11ta  41305  cdlemk11tc  41321