Theorem simp213 1312

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 1204	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1133	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 206  df-an 397  df-3an 1088

This theorem is referenced by:  cdleme27a  38381  cdlemk5u  38875  cdlemk6u  38876  cdlemk7u  38884  cdlemk11u  38885  cdlemk12u  38886  cdlemk7u-2N  38902  cdlemk11u-2N  38903  cdlemk12u-2N  38904  cdlemk20-2N  38906  cdlemk22  38907  cdlemk22-3  38915  cdlemk33N  38923  cdlemk53b  38970  cdlemk53  38971  cdlemk55a  38973  cdlemkyyN  38976  cdlemk43N  38977