Theorem simp213 1330

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 1222	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1150	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  cdleme27a  41065  cdlemk5u  41559  cdlemk6u  41560  cdlemk7u  41568  cdlemk11u  41569  cdlemk12u  41570  cdlemk7u-2N  41586  cdlemk11u-2N  41587  cdlemk12u-2N  41588  cdlemk20-2N  41590  cdlemk22  41591  cdlemk22-3  41599  cdlemk33N  41607  cdlemk53b  41654  cdlemk53  41655  cdlemk55a  41657  cdlemkyyN  41660  cdlemk43N  41661