Theorem simp133 1310

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

Assertion

Ref	Expression
simp133	⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Proof of Theorem simp133

Step	Hyp	Ref	Expression
1		simp33 1211	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

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:  tsmsxp  24109  ax5seglem3  28876  exatleN  39365  3atlem1  39444  3atlem2  39445  3atlem6  39449  4atlem11b  39569  4atlem12b  39572  lplncvrlvol2  39576  dalemuea  39592  dath2  39698  4atexlemex6  40035  cdleme22f2  40308  cdleme22g  40309  cdlemg7aN  40586  cdlemg31c  40660  cdlemg36  40675  cdlemj1  40782  cdlemj2  40783  cdlemk23-3  40863  cdlemk26b-3  40866