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  41615  cdlemk5u  42109  cdlemk6u  42110  cdlemk7u  42118  cdlemk11u  42119  cdlemk12u  42120  cdlemk7u-2N  42136  cdlemk11u-2N  42137  cdlemk12u-2N  42138  cdlemk20-2N  42140  cdlemk22  42141  cdlemk22-3  42149  cdlemk33N  42157  cdlemk53b  42204  cdlemk53  42205  cdlemk55a  42207  cdlemkyyN  42210  cdlemk43N  42211