Theorem simp213 1315

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

Assertion

Ref	Expression
simp213	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp213

Step	Hyp	Ref	Expression
1		simp13 1207	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1135	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

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  40831  cdlemk5u  41325  cdlemk6u  41326  cdlemk7u  41334  cdlemk11u  41335  cdlemk12u  41336  cdlemk7u-2N  41352  cdlemk11u-2N  41353  cdlemk12u-2N  41354  cdlemk20-2N  41356  cdlemk22  41357  cdlemk22-3  41365  cdlemk33N  41373  cdlemk53b  41420  cdlemk53  41421  cdlemk55a  41423  cdlemkyyN  41426  cdlemk43N  41427