Theorem simp321 1323

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 1206	. 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  39653  dalempnes  39654  dalemrot  39660  dath2  39740  cdleme18d  40298  cdleme20i  40320  cdleme20j  40321  cdleme20l2  40324  cdleme20l  40325  cdleme20m  40326  cdleme20  40327  cdleme21j  40339  cdleme22eALTN  40348  cdlemk16a  40859  cdlemk12u-2N  40893  cdlemk21-2N  40894  cdlemk22  40896  cdlemk31  40899  cdlemk32  40900  cdlemk11ta  40932  cdlemk11tc  40948