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  24130  ax5seglem3  29014  exatleN  39864  3atlem1  39943  3atlem2  39944  3atlem6  39948  4atlem11b  40068  4atlem12b  40071  lplncvrlvol2  40075  dalemuea  40091  dath2  40197  4atexlemex6  40534  cdleme22f2  40807  cdleme22g  40808  cdlemg7aN  41085  cdlemg31c  41159  cdlemg36  41174  cdlemj1  41281  cdlemj2  41282  cdlemk23-3  41362  cdlemk26b-3  41365