Theorem simp321 1322

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 1205	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1134	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1086

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 1088

This theorem is referenced by:  dalemcnes  37664  dalempnes  37665  dalemrot  37671  dath2  37751  cdleme18d  38309  cdleme20i  38331  cdleme20j  38332  cdleme20l2  38335  cdleme20l  38336  cdleme20m  38337  cdleme20  38338  cdleme21j  38350  cdleme22eALTN  38359  cdlemk16a  38870  cdlemk12u-2N  38904  cdlemk21-2N  38905  cdlemk22  38907  cdlemk31  38910  cdlemk32  38911  cdlemk11ta  38943  cdlemk11tc  38959