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 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  8175  mapxpen  9183  lsmcv  21143  pmatcollpw2  22784  sltlpss  27945  btwnconn1lem4  36091  linethru  36154  hlrelat3  39414  cvrval3  39415  cvrval4N  39416  2atlt  39441  atbtwnex  39450  1cvratlt  39476  atcvrlln2  39521  atcvrlln  39522  2llnmat  39526  lvolnlelpln  39587  lnjatN  39782  lncmp  39785  cdlemd9  40208  dihord5b  41261  dihmeetALTN  41329  mapdrvallem2  41647  itschlc0xyqsol  48688