Theorem simp1l1 1348

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 1225	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant1 1127	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1072

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 197  df-an 385  df-3an 1074

This theorem is referenced by:  mapxpen  8283  lsmcv  19335  archiabl  30053  trisegint  32433  linethru  32558  hlrelat3  35193  cvrval3  35194  cvrval4N  35195  2atlt  35220  atbtwnex  35229  1cvratlt  35255  atcvrlln2  35300  atcvrlln  35301  2llnmat  35305  lplnexllnN  35345  lvolnlelpln  35366  lnjatN  35561  lncvrat  35563  lncmp  35564  cdlemd9  35988  dihord5b  37042  dihmeetALTN  37110  dih1dimatlem0  37111  mapdrvallem2  37428