Theorem simp323 1326

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 1209	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

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:  dalemrot  39696  dath2  39776  cdleme18d  40334  cdleme20i  40356  cdleme20j  40357  cdleme20l2  40360  cdleme20l  40361  cdleme20m  40362  cdleme20  40363  cdleme21j  40375  cdleme22eALTN  40384  cdleme26eALTN  40400  cdlemk16a  40895  cdlemk12u-2N  40929  cdlemk21-2N  40930  cdlemk22  40932  cdlemk31  40935  cdlemk11ta  40968