Theorem simp322 1341

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 1224	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1151	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  dalemqnet  40315  dalemrot  40320  dath2  40400  cdleme18d  40958  cdleme20i  40980  cdleme20j  40981  cdleme20l2  40984  cdleme20l  40985  cdleme20m  40986  cdleme20  40987  cdleme21j  40999  cdleme22eALTN  41008  cdleme26eALTN  41024  cdlemk16a  41519  cdlemk12u-2N  41553  cdlemk21-2N  41554  cdlemk22  41556  cdlemk31  41559  cdlemk32  41560  cdlemk11ta  41592  cdlemk11tc  41608