Theorem simp132 1311

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 1212	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant1 1134	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 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:  ax5seglem3  29016  3atlem1  39853  3atlem2  39854  3atlem5  39857  2llnjaN  39936  4atlem11b  39978  4atlem12b  39981  lplncvrlvol2  39985  dalemtea  40000  dath2  40107  cdlemblem  40163  dalawlem1  40241  lhpexle3lem  40381  4atexlemex6  40444  cdleme22f2  40717  cdleme22g  40718  cdlemg7aN  40995  cdlemg34  41082  cdlemj1  41191  cdlemk23-3  41272  cdlemk25-3  41274  cdlemk26b-3  41275