Theorem simp1l2 1267

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 1192	. 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 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  8191  mapxpen  9209  lsmcv  21166  pmatcollpw2  22805  sltlpss  27963  btwnconn1lem4  36054  linethru  36117  hlrelat3  39369  cvrval3  39370  cvrval4N  39371  2atlt  39396  atbtwnex  39405  1cvratlt  39431  atcvrlln2  39476  atcvrlln  39477  2llnmat  39481  lvolnlelpln  39542  lnjatN  39737  lncmp  39740  cdlemd9  40163  dihord5b  41216  dihmeetALTN  41284  mapdrvallem2  41602  itschlc0xyqsol  48501