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  24048  ax5seglem3  28864  exatleN  39393  3atlem1  39472  3atlem2  39473  3atlem6  39477  4atlem11b  39597  4atlem12b  39600  lplncvrlvol2  39604  dalemuea  39620  dath2  39726  4atexlemex6  40063  cdleme22f2  40336  cdleme22g  40337  cdlemg7aN  40614  cdlemg31c  40688  cdlemg36  40703  cdlemj1  40810  cdlemj2  40811  cdlemk23-3  40891  cdlemk26b-3  40894