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  24059  ax5seglem3  28895  exatleN  39403  3atlem1  39482  3atlem2  39483  3atlem6  39487  4atlem11b  39607  4atlem12b  39610  lplncvrlvol2  39614  dalemuea  39630  dath2  39736  4atexlemex6  40073  cdleme22f2  40346  cdleme22g  40347  cdlemg7aN  40624  cdlemg31c  40698  cdlemg36  40713  cdlemj1  40820  cdlemj2  40821  cdlemk23-3  40901  cdlemk26b-3  40904