Theorem simp1l3 1268

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 1193	. 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 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  8191  btwnconn1lem7  36057  btwnconn1lem12  36062  linethru  36117  hlrelat3  39369  cvrval3  39370  2atlt  39396  atbtwnex  39405  1cvratlt  39431  2llnmat  39481  lplnexllnN  39521  4atlem11  39566  lnjatN  39737  lncvrat  39739  lncmp  39740  cdlemd9  40163  dihord5b  41216  dihmeetALTN  41284  dih1dimatlem0  41285  mapdrvallem2  41602  grumnudlem  44254  itsclc0yqsol  48498  itschlc0xyqsol  48501