Theorem simp323 1332

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 1215	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1141	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  dalemrot  40149  dath2  40229  cdleme18d  40787  cdleme20i  40809  cdleme20j  40810  cdleme20l2  40813  cdleme20l  40814  cdleme20m  40815  cdleme20  40816  cdleme21j  40828  cdleme22eALTN  40837  cdleme26eALTN  40853  cdlemk16a  41348  cdlemk12u-2N  41382  cdlemk21-2N  41383  cdlemk22  41385  cdlemk31  41388  cdlemk11ta  41421