Theorem simp323 1327

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

Assertion

Ref	Expression
simp323	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Proof of Theorem simp323

Step	Hyp	Ref	Expression
1		simp23 1210	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1136	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 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:  dalemrot  40117  dath2  40197  cdleme18d  40755  cdleme20i  40777  cdleme20j  40778  cdleme20l2  40781  cdleme20l  40782  cdleme20m  40783  cdleme20  40784  cdleme21j  40796  cdleme22eALTN  40805  cdleme26eALTN  40821  cdlemk16a  41316  cdlemk12u-2N  41350  cdlemk21-2N  41351  cdlemk22  41353  cdlemk31  41356  cdlemk11ta  41389