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  24099  ax5seglem3  29004  exatleN  39664  3atlem1  39743  3atlem2  39744  3atlem6  39748  4atlem11b  39868  4atlem12b  39871  lplncvrlvol2  39875  dalemuea  39891  dath2  39997  4atexlemex6  40334  cdleme22f2  40607  cdleme22g  40608  cdlemg7aN  40885  cdlemg31c  40959  cdlemg36  40974  cdlemj1  41081  cdlemj2  41082  cdlemk23-3  41162  cdlemk26b-3  41165