Theorem simp322 1326

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 1209	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1136	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

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:  dalemqnet  40115  dalemrot  40120  dath2  40200  cdleme18d  40758  cdleme20i  40780  cdleme20j  40781  cdleme20l2  40784  cdleme20l  40785  cdleme20m  40786  cdleme20  40787  cdleme21j  40799  cdleme22eALTN  40808  cdleme26eALTN  40824  cdlemk16a  41319  cdlemk12u-2N  41353  cdlemk21-2N  41354  cdlemk22  41356  cdlemk31  41359  cdlemk32  41360  cdlemk11ta  41392  cdlemk11tc  41408