Theorem simp313 1323

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

Assertion

Ref	Expression
simp313	⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜒)

Proof of Theorem simp313

Step	Hyp	Ref	Expression
1		simp13 1206	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1086

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  dalemrot  39651  dalem5  39661  dalem-cly  39665  dath2  39731  cdleme26e  40353  cdleme38m  40457  cdleme38n  40458  cdlemg28b  40697  cdlemg28  40698  cdlemk7  40842  cdlemk11  40843  cdlemk12  40844  cdlemk7u  40864  cdlemk11u  40865  cdlemk12u  40866  cdlemk22  40887  cdlemk23-3  40896  cdlemk25-3  40898