Theorem simp213 1311

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 1203	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1132	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  cdleme27a  38308  cdlemk5u  38802  cdlemk6u  38803  cdlemk7u  38811  cdlemk11u  38812  cdlemk12u  38813  cdlemk7u-2N  38829  cdlemk11u-2N  38830  cdlemk12u-2N  38831  cdlemk20-2N  38833  cdlemk22  38834  cdlemk22-3  38842  cdlemk33N  38850  cdlemk53b  38897  cdlemk53  38898  cdlemk55a  38900  cdlemkyyN  38903  cdlemk43N  38904