Theorem simp1l3 1267

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp1l3	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Proof of Theorem simp1l3

Step	Hyp	Ref	Expression
1		simpl3 1192	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒)
2	1	3ad2ant1 1132	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1088

This theorem is referenced by:  btwnconn1lem7  34395  btwnconn1lem12  34400  linethru  34455  hlrelat3  37426  cvrval3  37427  2atlt  37453  atbtwnex  37462  1cvratlt  37488  2llnmat  37538  lplnexllnN  37578  4atlem11  37623  lnjatN  37794  lncvrat  37796  lncmp  37797  cdlemd9  38220  dihord5b  39273  dihmeetALTN  39341  dih1dimatlem0  39342  mapdrvallem2  39659  grumnudlem  41903  itsclc0yqsol  46110  itschlc0xyqsol  46113