Theorem simp1l2 1263

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 1188	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	3ad2ant1 1129	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  mapxpen  8669  lsmcv  19896  pmatcollpw2  21369  btwnconn1lem4  33558  linethru  33621  hlrelat3  36580  cvrval3  36581  cvrval4N  36582  2atlt  36607  atbtwnex  36616  1cvratlt  36642  atcvrlln2  36687  atcvrlln  36688  2llnmat  36692  lvolnlelpln  36753  lnjatN  36948  lncmp  36951  cdlemd9  37374  dihord5b  38427  dihmeetALTN  38495  mapdrvallem2  38813  itschlc0xyqsol  44839