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 396  df-3an 1087

This theorem is referenced by:  dalemcnes  37591  dalempnes  37592  dalemrot  37598  dath2  37678  cdleme18d  38236  cdleme20i  38258  cdleme20j  38259  cdleme20l2  38262  cdleme20l  38263  cdleme20m  38264  cdleme20  38265  cdleme21j  38277  cdleme22eALTN  38286  cdlemk16a  38797  cdlemk12u-2N  38831  cdlemk21-2N  38832  cdlemk22  38834  cdlemk31  38837  cdlemk32  38838  cdlemk11ta  38870  cdlemk11tc  38886