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  28911  3atlem1  39603  3atlem2  39604  3atlem5  39607  2llnjaN  39686  4atlem11b  39728  4atlem12b  39731  lplncvrlvol2  39735  dalemtea  39750  dath2  39857  cdlemblem  39913  dalawlem1  39991  lhpexle3lem  40131  4atexlemex6  40194  cdleme22f2  40467  cdleme22g  40468  cdlemg7aN  40745  cdlemg34  40832  cdlemj1  40941  cdlemk23-3  41022  cdlemk25-3  41024  cdlemk26b-3  41025