Theorem simp323 1323

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

Assertion

Ref	Expression
simp323	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Proof of Theorem simp323

Step	Hyp	Ref	Expression
1		simp23 1206	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1133	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

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:  dalemrot  37650  dath2  37730  cdleme18d  38288  cdleme20i  38310  cdleme20j  38311  cdleme20l2  38314  cdleme20l  38315  cdleme20m  38316  cdleme20  38317  cdleme21j  38329  cdleme22eALTN  38338  cdleme26eALTN  38354  cdlemk16a  38849  cdlemk12u-2N  38883  cdlemk21-2N  38884  cdlemk22  38886  cdlemk31  38889  cdlemk11ta  38922