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 1133	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1086

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 1088

This theorem is referenced by:  tsmsxp  24065  ax5seglem3  28904  exatleN  39443  3atlem1  39522  3atlem2  39523  3atlem6  39527  4atlem11b  39647  4atlem12b  39650  lplncvrlvol2  39654  dalemuea  39670  dath2  39776  4atexlemex6  40113  cdleme22f2  40386  cdleme22g  40387  cdlemg7aN  40664  cdlemg31c  40738  cdlemg36  40753  cdlemj1  40860  cdlemj2  40861  cdlemk23-3  40941  cdlemk26b-3  40944