Theorem simp321 1321

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 1204	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1133	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1085

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 206  df-an 395  df-3an 1087

This theorem is referenced by:  dalemcnes  38824  dalempnes  38825  dalemrot  38831  dath2  38911  cdleme18d  39469  cdleme20i  39491  cdleme20j  39492  cdleme20l2  39495  cdleme20l  39496  cdleme20m  39497  cdleme20  39498  cdleme21j  39510  cdleme22eALTN  39519  cdlemk16a  40030  cdlemk12u-2N  40064  cdlemk21-2N  40065  cdlemk22  40067  cdlemk31  40070  cdlemk32  40071  cdlemk11ta  40103  cdlemk11tc  40119