Theorem simp131 1310

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 1211	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant1 1134	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1087

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 1089

This theorem is referenced by:  ax5seglem3  29016  exatleN  39780  3atlem1  39859  3atlem2  39860  3atlem5  39863  2llnjaN  39942  4atlem11b  39984  4atlem12b  39987  lplncvrlvol2  39991  dalemsea  40005  dath2  40113  cdlemblem  40169  dalawlem1  40247  lhpexle3lem  40387  4atexlemex6  40450  cdleme22f2  40723  cdleme22g  40724  cdlemg7aN  41001  cdlemg34  41088  cdlemj1  41197  cdlemk23-3  41278  cdlemk25-3  41280  cdlemk26b-3  41281  cdleml3N  41354