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  28876  exatleN  39383  3atlem1  39462  3atlem2  39463  3atlem5  39466  2llnjaN  39545  4atlem11b  39587  4atlem12b  39590  lplncvrlvol2  39594  dalemsea  39608  dath2  39716  cdlemblem  39772  dalawlem1  39850  lhpexle3lem  39990  4atexlemex6  40053  cdleme22f2  40326  cdleme22g  40327  cdlemg7aN  40604  cdlemg34  40691  cdlemj1  40800  cdlemk23-3  40881  cdlemk25-3  40883  cdlemk26b-3  40884  cdleml3N  40957