Theorem simp321 1323

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 1206	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1135	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 206  df-an 397  df-3an 1089

This theorem is referenced by:  dalemcnes  38324  dalempnes  38325  dalemrot  38331  dath2  38411  cdleme18d  38969  cdleme20i  38991  cdleme20j  38992  cdleme20l2  38995  cdleme20l  38996  cdleme20m  38997  cdleme20  38998  cdleme21j  39010  cdleme22eALTN  39019  cdlemk16a  39530  cdlemk12u-2N  39564  cdlemk21-2N  39565  cdlemk22  39567  cdlemk31  39570  cdlemk32  39571  cdlemk11ta  39603  cdlemk11tc  39619