Theorem simp322 1325

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

Assertion

Ref	Expression
simp322	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simp322

Step	Hyp	Ref	Expression
1		simp22 1208	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

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:  dalemqnet  39851  dalemrot  39856  dath2  39936  cdleme18d  40494  cdleme20i  40516  cdleme20j  40517  cdleme20l2  40520  cdleme20l  40521  cdleme20m  40522  cdleme20  40523  cdleme21j  40535  cdleme22eALTN  40544  cdleme26eALTN  40560  cdlemk16a  41055  cdlemk12u-2N  41089  cdlemk21-2N  41090  cdlemk22  41092  cdlemk31  41095  cdlemk32  41096  cdlemk11ta  41128  cdlemk11tc  41144