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  8149  btwnconn1lem7  36111  btwnconn1lem12  36116  linethru  36171  hlrelat3  39431  cvrval3  39432  2atlt  39458  atbtwnex  39467  1cvratlt  39493  2llnmat  39543  lplnexllnN  39583  4atlem11  39628  lnjatN  39799  lncvrat  39801  lncmp  39802  cdlemd9  40225  dihord5b  41278  dihmeetALTN  41346  dih1dimatlem0  41347  mapdrvallem2  41664  grumnudlem  44309  itsclc0yqsol  48744  itschlc0xyqsol  48747