Theorem simp131 1309

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp131	⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Proof of Theorem simp131

Step	Hyp	Ref	Expression
1		simp31 1210	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜑)

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  28953  exatleN  39603  3atlem1  39682  3atlem2  39683  3atlem5  39686  2llnjaN  39765  4atlem11b  39807  4atlem12b  39810  lplncvrlvol2  39814  dalemsea  39828  dath2  39936  cdlemblem  39992  dalawlem1  40070  lhpexle3lem  40210  4atexlemex6  40273  cdleme22f2  40546  cdleme22g  40547  cdlemg7aN  40824  cdlemg34  40911  cdlemj1  41020  cdlemk23-3  41101  cdlemk25-3  41103  cdlemk26b-3  41104  cdleml3N  41177