Theorem simp321 1204

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 1087	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1077	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

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:  dalemcnes  33954  dalempnes  33955  dalemrot  33961  dath2  34041  cdleme18d  34600  cdleme20i  34623  cdleme20j  34624  cdleme20l2  34627  cdleme20l  34628  cdleme20m  34629  cdleme20  34630  cdleme21j  34642  cdleme22eALTN  34651  cdlemk16a  35162  cdlemk12u-2N  35196  cdlemk21-2N  35197  cdlemk22  35199  cdlemk31  35202  cdlemk32  35203  cdlemk11ta  35235  cdlemk11tc  35251