Theorem simp213 1323

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 1215	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1143	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1095

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 209  df-an 399  df-3an 1097

This theorem is referenced by:  cdleme27a  40929  cdlemk5u  41423  cdlemk6u  41424  cdlemk7u  41432  cdlemk11u  41433  cdlemk12u  41434  cdlemk7u-2N  41450  cdlemk11u-2N  41451  cdlemk12u-2N  41452  cdlemk20-2N  41454  cdlemk22  41455  cdlemk22-3  41463  cdlemk33N  41471  cdlemk53b  41518  cdlemk53  41519  cdlemk55a  41521  cdlemkyyN  41524  cdlemk43N  41525