Theorem simp322 1323

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp322	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simp322

Step	Hyp	Ref	Expression
1		simp22 1206	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1134	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

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:  dalemqnet  39635  dalemrot  39640  dath2  39720  cdleme18d  40278  cdleme20i  40300  cdleme20j  40301  cdleme20l2  40304  cdleme20l  40305  cdleme20m  40306  cdleme20  40307  cdleme21j  40319  cdleme22eALTN  40328  cdleme26eALTN  40344  cdlemk16a  40839  cdlemk12u-2N  40873  cdlemk21-2N  40874  cdlemk22  40876  cdlemk31  40879  cdlemk32  40880  cdlemk11ta  40912  cdlemk11tc  40928