Theorem simp1l2 1266

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp1l2	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Proof of Theorem simp1l2

Step	Hyp	Ref	Expression
1		simpl2 1191	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	3ad2ant1 1132	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

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  pmatcollpw2  21927  sltlpss  34087  btwnconn1lem4  34392  linethru  34455  hlrelat3  37426  cvrval3  37427  cvrval4N  37428  2atlt  37453  atbtwnex  37462  1cvratlt  37488  atcvrlln2  37533  atcvrlln  37534  2llnmat  37538  lvolnlelpln  37599  lnjatN  37794  lncmp  37797  cdlemd9  38220  dihord5b  39273  dihmeetALTN  39341  mapdrvallem2  39659  itschlc0xyqsol  46113