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  28910  3atlem1  39528  3atlem2  39529  3atlem5  39532  2llnjaN  39611  4atlem11b  39653  4atlem12b  39656  lplncvrlvol2  39660  dalemtea  39675  dath2  39782  cdlemblem  39838  dalawlem1  39916  lhpexle3lem  40056  4atexlemex6  40119  cdleme22f2  40392  cdleme22g  40393  cdlemg7aN  40670  cdlemg34  40757  cdlemj1  40866  cdlemk23-3  40947  cdlemk25-3  40949  cdlemk26b-3  40950