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  8132  mapxpen  9113  hash7g  14458  lsmcv  21058  sltlpss  27826  archiabl  33159  trisegint  36023  linethru  36148  hlrelat3  39413  cvrval3  39414  cvrval4N  39415  2atlt  39440  atbtwnex  39449  1cvratlt  39475  atcvrlln2  39520  atcvrlln  39521  2llnmat  39525  lplnexllnN  39565  lvolnlelpln  39586  lnjatN  39781  lncvrat  39783  lncmp  39784  cdlemd9  40207  dihord5b  41260  dihmeetALTN  41328  dih1dimatlem0  41329  mapdrvallem2  41646  grumnudlem  44281