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 402  df-3an 1105

This theorem is used by:  cdleme27a  41305  cdlemk5u  41799  cdlemk6u  41800  cdlemk7u  41808  cdlemk11u  41809  cdlemk12u  41810  cdlemk7u-2N  41826  cdlemk11u-2N  41827  cdlemk12u-2N  41828  cdlemk20-2N  41830  cdlemk22  41831  cdlemk22-3  41839  cdlemk33N  41847  cdlemk53b  41894  cdlemk53  41895  cdlemk55a  41897  cdlemkyyN  41900  cdlemk43N  41901