Theorem simp1l3 1269

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 1194	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒)
2	1	3ad2ant1 1133	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ 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:  poxp3  8092  btwnconn1lem7  36287  btwnconn1lem12  36292  linethru  36347  hlrelat3  39682  cvrval3  39683  2atlt  39709  atbtwnex  39718  1cvratlt  39744  2llnmat  39794  lplnexllnN  39834  4atlem11  39879  lnjatN  40050  lncvrat  40052  lncmp  40053  cdlemd9  40476  dihord5b  41529  dihmeetALTN  41597  dih1dimatlem0  41598  mapdrvallem2  41915  grumnudlem  44536  itsclc0yqsol  49020  itschlc0xyqsol  49023