Theorem simp211 1313

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

Assertion

Ref	Expression
simp211	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Proof of Theorem simp211

Step	Hyp	Ref	Expression
1		simp11 1205	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant2 1135	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  cdleme27a  40813  cdlemk5u  41307  cdlemk6u  41308  cdlemk7u  41316  cdlemk11u  41317  cdlemk12u  41318  cdlemk7u-2N  41334  cdlemk11u-2N  41335  cdlemk12u-2N  41336  cdlemk20-2N  41338  cdlemk22  41339  cdlemk33N  41355  cdlemk53b  41402  cdlemk53  41403  cdlemk55a  41405  cdlemkyyN  41408  cdlemk43N  41409