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  8132  btwnconn1lem7  36088  btwnconn1lem12  36093  linethru  36148  hlrelat3  39413  cvrval3  39414  2atlt  39440  atbtwnex  39449  1cvratlt  39475  2llnmat  39525  lplnexllnN  39565  4atlem11  39610  lnjatN  39781  lncvrat  39783  lncmp  39784  cdlemd9  40207  dihord5b  41260  dihmeetALTN  41328  dih1dimatlem0  41329  mapdrvallem2  41646  grumnudlem  44281  itsclc0yqsol  48757  itschlc0xyqsol  48760