Theorem simp212 1325

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 1217	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1146	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  cdleme27a  40952  cdlemk5u  41446  cdlemk6u  41447  cdlemk7u  41455  cdlemk11u  41456  cdlemk12u  41457  cdlemk7u-2N  41473  cdlemk11u-2N  41474  cdlemk12u-2N  41475  cdlemk20-2N  41477  cdlemk22  41478  cdlemk22-3  41486  cdlemk33N  41494  cdlemk53b  41541  cdlemk53  41542  cdlemk55a  41544  cdlemkyyN  41547  cdlemk43N  41548