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  8090  mapxpen  9067  lsmcv  21066  pmatcollpw2  22681  sltlpss  27840  btwnconn1lem4  36066  linethru  36129  hlrelat3  39394  cvrval3  39395  cvrval4N  39396  2atlt  39421  atbtwnex  39430  1cvratlt  39456  atcvrlln2  39501  atcvrlln  39502  2llnmat  39506  lvolnlelpln  39567  lnjatN  39762  lncmp  39765  cdlemd9  40188  dihord5b  41241  dihmeetALTN  41309  mapdrvallem2  41627  itschlc0xyqsol  48756