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 1134	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 397   ∧ w3a 1088

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 398  df-3an 1090

This theorem is referenced by:  poxp3  8131  mapxpen  9139  lsmcv  20742  pmatcollpw2  22262  sltlpss  27381  btwnconn1lem4  35000  linethru  35063  hlrelat3  38221  cvrval3  38222  cvrval4N  38223  2atlt  38248  atbtwnex  38257  1cvratlt  38283  atcvrlln2  38328  atcvrlln  38329  2llnmat  38333  lvolnlelpln  38394  lnjatN  38589  lncmp  38592  cdlemd9  39015  dihord5b  40068  dihmeetALTN  40136  mapdrvallem2  40454  itschlc0xyqsol  47355