Theorem simp213 1320

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 1212	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1140	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  cdleme27a  40868  cdlemk5u  41362  cdlemk6u  41363  cdlemk7u  41371  cdlemk11u  41372  cdlemk12u  41373  cdlemk7u-2N  41389  cdlemk11u-2N  41390  cdlemk12u-2N  41391  cdlemk20-2N  41393  cdlemk22  41394  cdlemk22-3  41402  cdlemk33N  41410  cdlemk53b  41457  cdlemk53  41458  cdlemk55a  41460  cdlemkyyN  41463  cdlemk43N  41464