Theorem simp323 1322

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 1205	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1132	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1084

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 210  df-an 400  df-3an 1086

This theorem is referenced by:  dalemrot  36953  dath2  37033  cdleme18d  37591  cdleme20i  37613  cdleme20j  37614  cdleme20l2  37617  cdleme20l  37618  cdleme20m  37619  cdleme20  37620  cdleme21j  37632  cdleme22eALTN  37641  cdleme26eALTN  37657  cdlemk16a  38152  cdlemk12u-2N  38186  cdlemk21-2N  38187  cdlemk22  38189  cdlemk31  38192  cdlemk11ta  38225