Theorem simp323 1322

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 1205	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1132	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1084

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 206  df-an 396  df-3an 1086

This theorem is referenced by:  dalemrot  39018  dath2  39098  cdleme18d  39656  cdleme20i  39678  cdleme20j  39679  cdleme20l2  39682  cdleme20l  39683  cdleme20m  39684  cdleme20  39685  cdleme21j  39697  cdleme22eALTN  39706  cdleme26eALTN  39722  cdlemk16a  40217  cdlemk12u-2N  40251  cdlemk21-2N  40252  cdlemk22  40254  cdlemk31  40257  cdlemk11ta  40290