Theorem simp321 1324

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 1207	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

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:  dalemcnes  39639  dalempnes  39640  dalemrot  39646  dath2  39726  cdleme18d  40284  cdleme20i  40306  cdleme20j  40307  cdleme20l2  40310  cdleme20l  40311  cdleme20m  40312  cdleme20  40313  cdleme21j  40325  cdleme22eALTN  40334  cdlemk16a  40845  cdlemk12u-2N  40879  cdlemk21-2N  40880  cdlemk22  40882  cdlemk31  40885  cdlemk32  40886  cdlemk11ta  40918  cdlemk11tc  40934