Theorem simp133 1311

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 1212	. 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  24188  ax5seglem3  28972  exatleN  39401  3atlem1  39480  3atlem2  39481  3atlem6  39485  4atlem11b  39605  4atlem12b  39608  lplncvrlvol2  39612  dalemuea  39628  dath2  39734  4atexlemex6  40071  cdleme22f2  40344  cdleme22g  40345  cdlemg7aN  40622  cdlemg31c  40696  cdlemg36  40711  cdlemj1  40818  cdlemj2  40819  cdlemk23-3  40899  cdlemk26b-3  40902