Theorem simp133 1410

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 1269	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant1 1164	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1108

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 199  df-an 386  df-3an 1110

This theorem is referenced by:  tsmsxp  22286  ax5seglem3  26168  exatleN  35425  3atlem1  35504  3atlem2  35505  3atlem6  35509  4atlem11b  35629  4atlem12b  35632  lplncvrlvol2  35636  dalemuea  35652  dath2  35758  4atexlemex6  36095  cdleme22f2  36368  cdleme22g  36369  cdlemg7aN  36646  cdlemg31c  36720  cdlemg36  36735  cdlemj1  36842  cdlemj2  36843  cdlemk23-3  36923  cdlemk26b-3  36926