Theorem simp212 1319

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 1211	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1140	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  cdleme27a  40859  cdlemk5u  41353  cdlemk6u  41354  cdlemk7u  41362  cdlemk11u  41363  cdlemk12u  41364  cdlemk7u-2N  41380  cdlemk11u-2N  41381  cdlemk12u-2N  41382  cdlemk20-2N  41384  cdlemk22  41385  cdlemk22-3  41393  cdlemk33N  41401  cdlemk53b  41448  cdlemk53  41449  cdlemk55a  41451  cdlemkyyN  41454  cdlemk43N  41455