Theorem simp132 1409

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 1268	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant1 1164	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1108

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 199  df-an 386  df-3an 1110

This theorem is referenced by:  ax5seglem3  26168  3atlem1  35504  3atlem2  35505  3atlem5  35508  2llnjaN  35587  4atlem11b  35629  4atlem12b  35632  lplncvrlvol2  35636  dalemtea  35651  dath2  35758  cdlemblem  35814  dalawlem1  35892  lhpexle3lem  36032  4atexlemex6  36095  cdleme22f2  36368  cdleme22g  36369  cdlemg7aN  36646  cdlemg34  36733  cdlemj1  36842  cdlemk23-3  36923  cdlemk25-3  36925  cdlemk26b-3  36926