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  24018  ax5seglem3  28834  exatleN  39371  3atlem1  39450  3atlem2  39451  3atlem6  39455  4atlem11b  39575  4atlem12b  39578  lplncvrlvol2  39582  dalemuea  39598  dath2  39704  4atexlemex6  40041  cdleme22f2  40314  cdleme22g  40315  cdlemg7aN  40592  cdlemg31c  40666  cdlemg36  40681  cdlemj1  40788  cdlemj2  40789  cdlemk23-3  40869  cdlemk26b-3  40872