Theorem simp323 1342

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 1225	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1151	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1101

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 1103

This theorem is referenced by:  dalemrot  40316  dath2  40396  cdleme18d  40954  cdleme20i  40976  cdleme20j  40977  cdleme20l2  40980  cdleme20l  40981  cdleme20m  40982  cdleme20  40983  cdleme21j  40995  cdleme22eALTN  41004  cdleme26eALTN  41020  cdlemk16a  41515  cdlemk12u-2N  41549  cdlemk21-2N  41550  cdlemk22  41552  cdlemk31  41555  cdlemk11ta  41588