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  8083  btwnconn1lem7  36071  btwnconn1lem12  36076  linethru  36131  hlrelat3  39395  cvrval3  39396  2atlt  39422  atbtwnex  39431  1cvratlt  39457  2llnmat  39507  lplnexllnN  39547  4atlem11  39592  lnjatN  39763  lncvrat  39765  lncmp  39766  cdlemd9  40189  dihord5b  41242  dihmeetALTN  41310  dih1dimatlem0  41311  mapdrvallem2  41628  grumnudlem  44262  itsclc0yqsol  48753  itschlc0xyqsol  48756