Theorem simp131 1307

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 1208	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant1 1132	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  28961  exatleN  39387  3atlem1  39466  3atlem2  39467  3atlem5  39470  2llnjaN  39549  4atlem11b  39591  4atlem12b  39594  lplncvrlvol2  39598  dalemsea  39612  dath2  39720  cdlemblem  39776  dalawlem1  39854  lhpexle3lem  39994  4atexlemex6  40057  cdleme22f2  40330  cdleme22g  40331  cdlemg7aN  40608  cdlemg34  40695  cdlemj1  40804  cdlemk23-3  40885  cdlemk25-3  40887  cdlemk26b-3  40888  cdleml3N  40961