Theorem simp1l2 1268

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 1193	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	3ad2ant1 1133	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

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  8092  mapxpen  9071  lsmcv  21096  pmatcollpw2  22722  ltslpss  27904  btwnconn1lem4  36284  linethru  36347  hlrelat3  39672  cvrval3  39673  cvrval4N  39674  2atlt  39699  atbtwnex  39708  1cvratlt  39734  atcvrlln2  39779  atcvrlln  39780  2llnmat  39784  lvolnlelpln  39845  lnjatN  40040  lncmp  40043  cdlemd9  40466  dihord5b  41519  dihmeetALTN  41587  mapdrvallem2  41905  itschlc0xyqsol  49013