Theorem simp212 1331

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp212	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Proof of Theorem simp212

Step	Hyp	Ref	Expression
1		simp12 1223	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1152	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  cdleme27a  41531  cdlemk5u  42025  cdlemk6u  42026  cdlemk7u  42034  cdlemk11u  42035  cdlemk12u  42036  cdlemk7u-2N  42052  cdlemk11u-2N  42053  cdlemk12u-2N  42054  cdlemk20-2N  42056  cdlemk22  42057  cdlemk22-3  42065  cdlemk33N  42073  cdlemk53b  42120  cdlemk53  42121  cdlemk55a  42123  cdlemkyyN  42126  cdlemk43N  42127