Theorem simp1l1 1265

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 1190	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant1 1132	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  8174  mapxpen  9182  hash7g  14522  lsmcv  21161  sltlpss  27960  archiabl  33188  trisegint  36010  linethru  36135  hlrelat3  39395  cvrval3  39396  cvrval4N  39397  2atlt  39422  atbtwnex  39431  1cvratlt  39457  atcvrlln2  39502  atcvrlln  39503  2llnmat  39507  lplnexllnN  39547  lvolnlelpln  39568  lnjatN  39763  lncvrat  39765  lncmp  39766  cdlemd9  40189  dihord5b  41242  dihmeetALTN  41310  dih1dimatlem0  41311  mapdrvallem2  41628  grumnudlem  44281