Theorem simp313 1335

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 1218	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1147	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 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:  dalemrot  40242  dalem5  40252  dalem-cly  40256  dath2  40322  cdleme26e  40944  cdleme38m  41048  cdleme38n  41049  cdlemg28b  41288  cdlemg28  41289  cdlemk7  41433  cdlemk11  41434  cdlemk12  41435  cdlemk7u  41455  cdlemk11u  41456  cdlemk12u  41457  cdlemk22  41478  cdlemk23-3  41487  cdlemk25-3  41489