Theorem simp3lr 1246

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp3lr	⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Proof of Theorem simp3lr

Step	Hyp	Ref	Expression
1		simplr 768	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 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:  f1oiso2  7293  omeu  8510  ntrivcvgmul  15827  tsmsxp  24058  tgqioo  24704  ovolunlem2  25415  plyadd  26138  plymul  26139  coeeu  26146  nosupbnd1lem2  27637  noinfbnd1lem2  27652  tghilberti2  28601  btwnconn1lem2  36061  btwnconn1lem3  36062  btwnconn1lem4  36063  athgt  39435  2llnjN  39546  4atlem12b  39590  lncmp  39762  cdlema2N  39771  cdleme21ct  40308  cdleme24  40331  cdleme27a  40346  cdleme28  40352  cdleme42b  40457  cdlemf  40542  dihlsscpre  41213  dihord4  41237  dihord5apre  41241  pellex  42808  jm2.27  42981