Theorem simp323 1338

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 1221	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1147	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  dalemrot  40242  dath2  40322  cdleme18d  40880  cdleme20i  40902  cdleme20j  40903  cdleme20l2  40906  cdleme20l  40907  cdleme20m  40908  cdleme20  40909  cdleme21j  40921  cdleme22eALTN  40930  cdleme26eALTN  40946  cdlemk16a  41441  cdlemk12u-2N  41475  cdlemk21-2N  41476  cdlemk22  41478  cdlemk31  41481  cdlemk11ta  41514