Theorem simp1l3 1266

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 1191	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒)
2	1	3ad2ant1 1131	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  poxp3  8149  btwnconn1lem7  35683  btwnconn1lem12  35688  linethru  35743  hlrelat3  38879  cvrval3  38880  2atlt  38906  atbtwnex  38915  1cvratlt  38941  2llnmat  38991  lplnexllnN  39031  4atlem11  39076  lnjatN  39247  lncvrat  39249  lncmp  39250  cdlemd9  39673  dihord5b  40726  dihmeetALTN  40794  dih1dimatlem0  40795  mapdrvallem2  41112  grumnudlem  43716  itsclc0yqsol  47831  itschlc0xyqsol  47834