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  41425  cdlemk5u  41919  cdlemk6u  41920  cdlemk7u  41928  cdlemk11u  41929  cdlemk12u  41930  cdlemk7u-2N  41946  cdlemk11u-2N  41947  cdlemk12u-2N  41948  cdlemk20-2N  41950  cdlemk22  41951  cdlemk22-3  41959  cdlemk33N  41967  cdlemk53b  42014  cdlemk53  42015  cdlemk55a  42017  cdlemkyyN  42020  cdlemk43N  42021