Theorem simp213 1201

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 1093	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1083	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  cdleme27a  35655  cdlemk5u  36149  cdlemk6u  36150  cdlemk7u  36158  cdlemk11u  36159  cdlemk12u  36160  cdlemk7u-2N  36176  cdlemk11u-2N  36177  cdlemk12u-2N  36178  cdlemk20-2N  36180  cdlemk22  36181  cdlemk22-3  36189  cdlemk33N  36197  cdlemk53b  36244  cdlemk53  36245  cdlemk55a  36247  cdlemkyyN  36250  cdlemk43N  36251