Theorem simp321 1340

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 1223	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1151	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  dalemcnes  40314  dalempnes  40315  dalemrot  40321  dath2  40401  cdleme18d  40959  cdleme20i  40981  cdleme20j  40982  cdleme20l2  40985  cdleme20l  40986  cdleme20m  40987  cdleme20  40988  cdleme21j  41000  cdleme22eALTN  41009  cdlemk16a  41520  cdlemk12u-2N  41554  cdlemk21-2N  41555  cdlemk22  41557  cdlemk31  41560  cdlemk32  41561  cdlemk11ta  41593  cdlemk11tc  41609