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  28865  3atlem1  39484  3atlem2  39485  3atlem5  39488  2llnjaN  39567  4atlem11b  39609  4atlem12b  39612  lplncvrlvol2  39616  dalemtea  39631  dath2  39738  cdlemblem  39794  dalawlem1  39872  lhpexle3lem  40012  4atexlemex6  40075  cdleme22f2  40348  cdleme22g  40349  cdlemg7aN  40626  cdlemg34  40713  cdlemj1  40822  cdlemk23-3  40903  cdlemk25-3  40905  cdlemk26b-3  40906