Theorem simp132 1310

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

Assertion

Ref	Expression
simp132	⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Proof of Theorem simp132

Step	Hyp	Ref	Expression
1		simp32 1211	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜓)

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:  ax5seglem3  29004  3atlem1  39739  3atlem2  39740  3atlem5  39743  2llnjaN  39822  4atlem11b  39864  4atlem12b  39867  lplncvrlvol2  39871  dalemtea  39886  dath2  39993  cdlemblem  40049  dalawlem1  40127  lhpexle3lem  40267  4atexlemex6  40330  cdleme22f2  40603  cdleme22g  40604  cdlemg7aN  40881  cdlemg34  40968  cdlemj1  41077  cdlemk23-3  41158  cdlemk25-3  41160  cdlemk26b-3  41161