Theorem simp213 1314

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 1206	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1134	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  cdleme27a  40649  cdlemk5u  41143  cdlemk6u  41144  cdlemk7u  41152  cdlemk11u  41153  cdlemk12u  41154  cdlemk7u-2N  41170  cdlemk11u-2N  41171  cdlemk12u-2N  41172  cdlemk20-2N  41174  cdlemk22  41175  cdlemk22-3  41183  cdlemk33N  41191  cdlemk53b  41238  cdlemk53  41239  cdlemk55a  41241  cdlemkyyN  41244  cdlemk43N  41245