Theorem simp323 1344

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 1227	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1153	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1103

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 401  df-3an 1105

This theorem is referenced by:  dalemrot  40412  dath2  40492  cdleme18d  41050  cdleme20i  41072  cdleme20j  41073  cdleme20l2  41076  cdleme20l  41077  cdleme20m  41078  cdleme20  41079  cdleme21j  41091  cdleme22eALTN  41100  cdleme26eALTN  41116  cdlemk16a  41611  cdlemk12u-2N  41645  cdlemk21-2N  41646  cdlemk22  41648  cdlemk31  41651  cdlemk11ta  41684