Theorem simp322 1343

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

Assertion

Ref	Expression
simp322	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simp322

Step	Hyp	Ref	Expression
1		simp22 1226	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1153	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

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:  dalemqnet  40426  dalemrot  40431  dath2  40511  cdleme18d  41069  cdleme20i  41091  cdleme20j  41092  cdleme20l2  41095  cdleme20l  41096  cdleme20m  41097  cdleme20  41098  cdleme21j  41110  cdleme22eALTN  41119  cdleme26eALTN  41135  cdlemk16a  41630  cdlemk12u-2N  41664  cdlemk21-2N  41665  cdlemk22  41667  cdlemk31  41670  cdlemk32  41671  cdlemk11ta  41703  cdlemk11tc  41719