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  8147  btwnconn1lem7  36057  btwnconn1lem12  36062  linethru  36117  hlrelat3  39377  cvrval3  39378  2atlt  39404  atbtwnex  39413  1cvratlt  39439  2llnmat  39489  lplnexllnN  39529  4atlem11  39574  lnjatN  39745  lncvrat  39747  lncmp  39748  cdlemd9  40171  dihord5b  41224  dihmeetALTN  41292  dih1dimatlem0  41293  mapdrvallem2  41610  grumnudlem  44257  itsclc0yqsol  48692  itschlc0xyqsol  48695