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  39674  dalempnes  39675  dalemrot  39681  dath2  39761  cdleme18d  40319  cdleme20i  40341  cdleme20j  40342  cdleme20l2  40345  cdleme20l  40346  cdleme20m  40347  cdleme20  40348  cdleme21j  40360  cdleme22eALTN  40369  cdlemk16a  40880  cdlemk12u-2N  40914  cdlemk21-2N  40915  cdlemk22  40917  cdlemk31  40920  cdlemk32  40921  cdlemk11ta  40953  cdlemk11tc  40969