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  41240  cdlemk5u  41734  cdlemk6u  41735  cdlemk7u  41743  cdlemk11u  41744  cdlemk12u  41745  cdlemk7u-2N  41761  cdlemk11u-2N  41762  cdlemk12u-2N  41763  cdlemk20-2N  41765  cdlemk22  41766  cdlemk22-3  41774  cdlemk33N  41782  cdlemk53b  41829  cdlemk53  41830  cdlemk55a  41832  cdlemkyyN  41835  cdlemk43N  41836