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 396  df-3an 1088

This theorem is referenced by:  cdleme27a  39705  cdlemk5u  40199  cdlemk6u  40200  cdlemk7u  40208  cdlemk11u  40209  cdlemk12u  40210  cdlemk7u-2N  40226  cdlemk11u-2N  40227  cdlemk12u-2N  40228  cdlemk20-2N  40230  cdlemk22  40231  cdlemk22-3  40239  cdlemk33N  40247  cdlemk53b  40294  cdlemk53  40295  cdlemk55a  40297  cdlemkyyN  40300  cdlemk43N  40301