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 1134	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

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  8175  mapxpen  9183  hash7g  14525  lsmcv  21143  sltlpss  27945  archiabl  33205  trisegint  36029  linethru  36154  hlrelat3  39414  cvrval3  39415  cvrval4N  39416  2atlt  39441  atbtwnex  39450  1cvratlt  39476  atcvrlln2  39521  atcvrlln  39522  2llnmat  39526  lplnexllnN  39566  lvolnlelpln  39587  lnjatN  39782  lncvrat  39784  lncmp  39785  cdlemd9  40208  dihord5b  41261  dihmeetALTN  41329  dih1dimatlem0  41330  mapdrvallem2  41647  grumnudlem  44304