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 1136	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1089

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 210  df-an 400  df-3an 1091

This theorem is referenced by:  cdleme27a  38118  cdlemk5u  38612  cdlemk6u  38613  cdlemk7u  38621  cdlemk11u  38622  cdlemk12u  38623  cdlemk7u-2N  38639  cdlemk11u-2N  38640  cdlemk12u-2N  38641  cdlemk20-2N  38643  cdlemk22  38644  cdlemk22-3  38652  cdlemk33N  38660  cdlemk53b  38707  cdlemk53  38708  cdlemk55a  38710  cdlemkyyN  38713  cdlemk43N  38714