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  40821  dath2  40901  cdleme18d  41459  cdleme20i  41481  cdleme20j  41482  cdleme20l2  41485  cdleme20l  41486  cdleme20m  41487  cdleme20  41488  cdleme21j  41500  cdleme22eALTN  41509  cdleme26eALTN  41525  cdlemk16a  42020  cdlemk12u-2N  42054  cdlemk21-2N  42055  cdlemk22  42057  cdlemk31  42060  cdlemk11ta  42093