Theorem simp213 1328

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 1220	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1148	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1099

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 400  df-3an 1101

This theorem is referenced by:  cdleme27a  40992  cdlemk5u  41486  cdlemk6u  41487  cdlemk7u  41495  cdlemk11u  41496  cdlemk12u  41497  cdlemk7u-2N  41513  cdlemk11u-2N  41514  cdlemk12u-2N  41515  cdlemk20-2N  41517  cdlemk22  41518  cdlemk22-3  41526  cdlemk33N  41534  cdlemk53b  41581  cdlemk53  41582  cdlemk55a  41584  cdlemkyyN  41587  cdlemk43N  41588