Theorem simp133 1312

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 1213	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant1 1134	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

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:  tsmsxp  24111  ax5seglem3  29016  exatleN  39777  3atlem1  39856  3atlem2  39857  3atlem6  39861  4atlem11b  39981  4atlem12b  39984  lplncvrlvol2  39988  dalemuea  40004  dath2  40110  4atexlemex6  40447  cdleme22f2  40720  cdleme22g  40721  cdlemg7aN  40998  cdlemg31c  41072  cdlemg36  41087  cdlemj1  41194  cdlemj2  41195  cdlemk23-3  41275  cdlemk26b-3  41278