Theorem simp1l1 1267

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp1l1	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Proof of Theorem simp1l1

Step	Hyp	Ref	Expression
1		simpl1 1192	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

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  8092  mapxpen  9071  hash7g  14409  lsmcv  21096  ltslpss  27904  archiabl  33280  trisegint  36222  linethru  36347  hlrelat3  39672  cvrval3  39673  cvrval4N  39674  2atlt  39699  atbtwnex  39708  1cvratlt  39734  atcvrlln2  39779  atcvrlln  39780  2llnmat  39784  lplnexllnN  39824  lvolnlelpln  39845  lnjatN  40040  lncvrat  40042  lncmp  40043  cdlemd9  40466  dihord5b  41519  dihmeetALTN  41587  dih1dimatlem0  41588  mapdrvallem2  41905  grumnudlem  44526