Theorem simp322 1326

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 1209	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1137	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1089

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 1091

This theorem is referenced by:  dalemqnet  37352  dalemrot  37357  dath2  37437  cdleme18d  37995  cdleme20i  38017  cdleme20j  38018  cdleme20l2  38021  cdleme20l  38022  cdleme20m  38023  cdleme20  38024  cdleme21j  38036  cdleme22eALTN  38045  cdleme26eALTN  38061  cdlemk16a  38556  cdlemk12u-2N  38590  cdlemk21-2N  38591  cdlemk22  38593  cdlemk31  38596  cdlemk32  38597  cdlemk11ta  38629  cdlemk11tc  38645