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  24042  ax5seglem3  28858  exatleN  39398  3atlem1  39477  3atlem2  39478  3atlem6  39482  4atlem11b  39602  4atlem12b  39605  lplncvrlvol2  39609  dalemuea  39625  dath2  39731  4atexlemex6  40068  cdleme22f2  40341  cdleme22g  40342  cdlemg7aN  40619  cdlemg31c  40693  cdlemg36  40708  cdlemj1  40815  cdlemj2  40816  cdlemk23-3  40896  cdlemk26b-3  40899