Theorem simp313 1319

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 1202	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1132	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 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 210  df-an 400  df-3an 1086

This theorem is referenced by:  dalemrot  36953  dalem5  36963  dalem-cly  36967  dath2  37033  cdleme26e  37655  cdleme38m  37759  cdleme38n  37760  cdlemg28b  37999  cdlemg28  38000  cdlemk7  38144  cdlemk11  38145  cdlemk12  38146  cdlemk7u  38166  cdlemk11u  38167  cdlemk12u  38168  cdlemk22  38189  cdlemk23-3  38198  cdlemk25-3  38200