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  39856  3atlem2  39857  3atlem5  39860  2llnjaN  39939  4atlem11b  39981  4atlem12b  39984  lplncvrlvol2  39988  dalemtea  40003  dath2  40110  cdlemblem  40166  dalawlem1  40244  lhpexle3lem  40384  4atexlemex6  40447  cdleme22f2  40720  cdleme22g  40721  cdlemg7aN  40998  cdlemg34  41085  cdlemj1  41194  cdlemk23-3  41275  cdlemk25-3  41277  cdlemk26b-3  41278