Theorem simp323 1425

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 1266	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1166	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1108

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 199  df-an 386  df-3an 1110

This theorem is referenced by:  dalemrot  35678  dath2  35758  cdleme18d  36316  cdleme20i  36338  cdleme20j  36339  cdleme20l2  36342  cdleme20l  36343  cdleme20m  36344  cdleme20  36345  cdleme21j  36357  cdleme22eALTN  36366  cdleme26eALTN  36382  cdlemk16a  36877  cdlemk12u-2N  36911  cdlemk21-2N  36912  cdlemk22  36914  cdlemk31  36917  cdlemk11ta  36950