Theorem simp323 1326

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

Assertion

Ref	Expression
simp323	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Proof of Theorem simp323

Step	Hyp	Ref	Expression
1		simp23 1209	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  dalemrot  39676  dath2  39756  cdleme18d  40314  cdleme20i  40336  cdleme20j  40337  cdleme20l2  40340  cdleme20l  40341  cdleme20m  40342  cdleme20  40343  cdleme21j  40355  cdleme22eALTN  40364  cdleme26eALTN  40380  cdlemk16a  40875  cdlemk12u-2N  40909  cdlemk21-2N  40910  cdlemk22  40912  cdlemk31  40915  cdlemk11ta  40948