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 1134	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  poxp3  8175  btwnconn1lem7  36094  btwnconn1lem12  36099  linethru  36154  hlrelat3  39414  cvrval3  39415  2atlt  39441  atbtwnex  39450  1cvratlt  39476  2llnmat  39526  lplnexllnN  39566  4atlem11  39611  lnjatN  39782  lncvrat  39784  lncmp  39785  cdlemd9  40208  dihord5b  41261  dihmeetALTN  41329  dih1dimatlem0  41330  mapdrvallem2  41647  grumnudlem  44304  itsclc0yqsol  48685  itschlc0xyqsol  48688