Theorem simp213 1313

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 1205	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1134	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  40324  cdlemk5u  40818  cdlemk6u  40819  cdlemk7u  40827  cdlemk11u  40828  cdlemk12u  40829  cdlemk7u-2N  40845  cdlemk11u-2N  40846  cdlemk12u-2N  40847  cdlemk20-2N  40849  cdlemk22  40850  cdlemk22-3  40858  cdlemk33N  40866  cdlemk53b  40913  cdlemk53  40914  cdlemk55a  40916  cdlemkyyN  40919  cdlemk43N  40920