Theorem simp333 1341

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 1224	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1147	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 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:  ivthALT  36656  dalemclrju  40221  dath2  40322  cdlema1N  40376  cdleme26eALTN  40946  cdlemk7u  41455  cdlemk11u  41456  cdlemk12u  41457  cdlemk22  41478  cdlemk23-3  41487  cdlemk33N  41494  cdlemk11ta  41514  cdlemk11tc  41530  cdlemk54  41543