Theorem simp133 1198

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 1099	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant1 1082	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  tsmsxp  21958  ax5seglem3  25811  exatleN  34690  3atlem1  34769  3atlem2  34770  3atlem6  34774  4atlem11b  34894  4atlem12b  34897  lplncvrlvol2  34901  dalemuea  34917  dath2  35023  4atexlemex6  35360  cdleme22f2  35635  cdleme22g  35636  cdlemg7aN  35913  cdlemg31c  35987  cdlemg36  36002  cdlemj1  36109  cdlemj2  36110  cdlemk23-3  36190  cdlemk26b-3  36193