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  8149  mapxpen  9157  hash7g  14504  lsmcv  21102  sltlpss  27871  archiabl  33196  trisegint  36046  linethru  36171  hlrelat3  39431  cvrval3  39432  cvrval4N  39433  2atlt  39458  atbtwnex  39467  1cvratlt  39493  atcvrlln2  39538  atcvrlln  39539  2llnmat  39543  lplnexllnN  39583  lvolnlelpln  39604  lnjatN  39799  lncvrat  39801  lncmp  39802  cdlemd9  40225  dihord5b  41278  dihmeetALTN  41346  dih1dimatlem0  41347  mapdrvallem2  41664  grumnudlem  44309