Theorem simp132 1394

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 1253	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant1 1128	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1072

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 197  df-an 385  df-3an 1074

This theorem is referenced by:  ax5seglem3  26010  3atlem1  35272  3atlem2  35273  3atlem5  35276  2llnjaN  35355  4atlem11b  35397  4atlem12b  35400  lplncvrlvol2  35404  dalemtea  35419  dath2  35526  cdlemblem  35582  dalawlem1  35660  lhpexle3lem  35800  4atexlemex6  35863  cdleme22f2  36137  cdleme22g  36138  cdlemg7aN  36415  cdlemg34  36502  cdlemj1  36611  cdlemk23-3  36692  cdlemk25-3  36694  cdlemk26b-3  36695