Theorem simp333 1325

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

Assertion

Ref	Expression
simp333	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simp333

Step	Hyp	Ref	Expression
1		simp33 1208	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1132	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 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 395  df-3an 1086

This theorem is referenced by:  ivthALT  35824  dalemclrju  39113  dath2  39214  cdlema1N  39268  cdleme26eALTN  39838  cdlemk7u  40347  cdlemk11u  40348  cdlemk12u  40349  cdlemk22  40370  cdlemk23-3  40379  cdlemk33N  40386  cdlemk11ta  40406  cdlemk11tc  40422  cdlemk54  40435