Theorem simp322 1325

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 1208	. 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  39654  dalemrot  39659  dath2  39739  cdleme18d  40297  cdleme20i  40319  cdleme20j  40320  cdleme20l2  40323  cdleme20l  40324  cdleme20m  40325  cdleme20  40326  cdleme21j  40338  cdleme22eALTN  40347  cdleme26eALTN  40363  cdlemk16a  40858  cdlemk12u-2N  40892  cdlemk21-2N  40893  cdlemk22  40895  cdlemk31  40898  cdlemk32  40899  cdlemk11ta  40931  cdlemk11tc  40947