Theorem simp321 1211

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

Assertion

Ref	Expression
simp321	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Proof of Theorem simp321

Step	Hyp	Ref	Expression
1		simp21 1094	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1084	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  dalemcnes  34936  dalempnes  34937  dalemrot  34943  dath2  35023  cdleme18d  35582  cdleme20i  35605  cdleme20j  35606  cdleme20l2  35609  cdleme20l  35610  cdleme20m  35611  cdleme20  35612  cdleme21j  35624  cdleme22eALTN  35633  cdlemk16a  36144  cdlemk12u-2N  36178  cdlemk21-2N  36179  cdlemk22  36181  cdlemk31  36184  cdlemk32  36185  cdlemk11ta  36217  cdlemk11tc  36233