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 1087

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 1089

This theorem is referenced by:  dalemcnes  39607  dalempnes  39608  dalemrot  39614  dath2  39694  cdleme18d  40252  cdleme20i  40274  cdleme20j  40275  cdleme20l2  40278  cdleme20l  40279  cdleme20m  40280  cdleme20  40281  cdleme21j  40293  cdleme22eALTN  40302  cdlemk16a  40813  cdlemk12u-2N  40847  cdlemk21-2N  40848  cdlemk22  40850  cdlemk31  40853  cdlemk32  40854  cdlemk11ta  40886  cdlemk11tc  40902