Theorem simp213 1315

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 1207	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1135	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1087

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 1089

This theorem is referenced by:  cdleme27a  40772  cdlemk5u  41266  cdlemk6u  41267  cdlemk7u  41275  cdlemk11u  41276  cdlemk12u  41277  cdlemk7u-2N  41293  cdlemk11u-2N  41294  cdlemk12u-2N  41295  cdlemk20-2N  41297  cdlemk22  41298  cdlemk22-3  41306  cdlemk33N  41314  cdlemk53b  41361  cdlemk53  41362  cdlemk55a  41364  cdlemkyyN  41367  cdlemk43N  41368