Theorem simp333 1428

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 1269	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1166	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 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:  ivthALT  32842  dalemclrju  35657  dath2  35758  cdlema1N  35812  cdleme26eALTN  36382  cdlemk7u  36891  cdlemk11u  36892  cdlemk12u  36893  cdlemk22  36914  cdlemk23-3  36923  cdlemk33N  36930  cdlemk11ta  36950  cdlemk11tc  36966  cdlemk54  36979