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 396   ∧ 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 206  df-an 397  df-3an 1088

This theorem is referenced by:  mapxpen  8930  lsmcv  20403  archiabl  31452  sltlpss  34087  trisegint  34330  linethru  34455  hlrelat3  37426  cvrval3  37427  cvrval4N  37428  2atlt  37453  atbtwnex  37462  1cvratlt  37488  atcvrlln2  37533  atcvrlln  37534  2llnmat  37538  lplnexllnN  37578  lvolnlelpln  37599  lnjatN  37794  lncvrat  37796  lncmp  37797  cdlemd9  38220  dihord5b  39273  dihmeetALTN  39341  dih1dimatlem0  39342  mapdrvallem2  39659  grumnudlem  41903