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  28904  exatleN  39443  3atlem1  39522  3atlem2  39523  3atlem5  39526  2llnjaN  39605  4atlem11b  39647  4atlem12b  39650  lplncvrlvol2  39654  dalemsea  39668  dath2  39776  cdlemblem  39832  dalawlem1  39910  lhpexle3lem  40050  4atexlemex6  40113  cdleme22f2  40386  cdleme22g  40387  cdlemg7aN  40664  cdlemg34  40751  cdlemj1  40860  cdlemk23-3  40941  cdlemk25-3  40943  cdlemk26b-3  40944  cdleml3N  41017