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)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  dalemrot  40694  dath2  40774  cdleme18d  41332  cdleme20i  41354  cdleme20j  41355  cdleme20l2  41358  cdleme20l  41359  cdleme20m  41360  cdleme20  41361  cdleme21j  41373  cdleme22eALTN  41382  cdleme26eALTN  41398  cdlemk16a  41893  cdlemk12u-2N  41927  cdlemk21-2N  41928  cdlemk22  41930  cdlemk31  41933  cdlemk11ta  41966