Theorem simp1l2 1266

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 1191	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	3ad2ant1 1132	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  8174  mapxpen  9182  lsmcv  21161  pmatcollpw2  22800  sltlpss  27960  btwnconn1lem4  36072  linethru  36135  hlrelat3  39395  cvrval3  39396  cvrval4N  39397  2atlt  39422  atbtwnex  39431  1cvratlt  39457  atcvrlln2  39502  atcvrlln  39503  2llnmat  39507  lvolnlelpln  39568  lnjatN  39763  lncmp  39766  cdlemd9  40189  dihord5b  41242  dihmeetALTN  41310  mapdrvallem2  41628  itschlc0xyqsol  48617