Theorem simp213 1332

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

Assertion

Ref	Expression
simp213	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp213

Step	Hyp	Ref	Expression
1		simp13 1224	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1152	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 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 401  df-3an 1105

This theorem is used by:  cdleme27a  41169  cdlemk5u  41663  cdlemk6u  41664  cdlemk7u  41672  cdlemk11u  41673  cdlemk12u  41674  cdlemk7u-2N  41690  cdlemk11u-2N  41691  cdlemk12u-2N  41692  cdlemk20-2N  41694  cdlemk22  41695  cdlemk22-3  41703  cdlemk33N  41711  cdlemk53b  41758  cdlemk53  41759  cdlemk55a  41761  cdlemkyyN  41764  cdlemk43N  41765