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  40096  dalempnes  40097  dalemrot  40103  dath2  40183  cdleme18d  40741  cdleme20i  40763  cdleme20j  40764  cdleme20l2  40767  cdleme20l  40768  cdleme20m  40769  cdleme20  40770  cdleme21j  40782  cdleme22eALTN  40791  cdlemk16a  41302  cdlemk12u-2N  41336  cdlemk21-2N  41337  cdlemk22  41339  cdlemk31  41342  cdlemk32  41343  cdlemk11ta  41375  cdlemk11tc  41391