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  7327  omeu  8549  ntrivcvgmul  15868  tsmsxp  24042  tgqioo  24688  ovolunlem2  25399  plyadd  26122  plymul  26123  coeeu  26130  nosupbnd1lem2  27621  noinfbnd1lem2  27636  tghilberti2  28565  btwnconn1lem2  36076  btwnconn1lem3  36077  btwnconn1lem4  36078  athgt  39450  2llnjN  39561  4atlem12b  39605  lncmp  39777  cdlema2N  39786  cdleme21ct  40323  cdleme24  40346  cdleme27a  40361  cdleme28  40367  cdleme42b  40472  cdlemf  40557  dihlsscpre  41228  dihord4  41252  dihord5apre  41256  pellex  42823  jm2.27  42997