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 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  24184  ax5seglem3  28964  exatleN  39361  3atlem1  39440  3atlem2  39441  3atlem6  39445  4atlem11b  39565  4atlem12b  39568  lplncvrlvol2  39572  dalemuea  39588  dath2  39694  4atexlemex6  40031  cdleme22f2  40304  cdleme22g  40305  cdlemg7aN  40582  cdlemg31c  40656  cdlemg36  40671  cdlemj1  40778  cdlemj2  40779  cdlemk23-3  40859  cdlemk26b-3  40862