Theorem simp3lr 1244

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 766	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1134	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1088

This theorem is referenced by:  f1oiso2  7273  omeu  8479  ntrivcvgmul  15705  tsmsxp  23404  tgqioo  24061  ovolunlem2  24760  plyadd  25476  plymul  25477  coeeu  25484  nosupbnd1lem2  26955  noinfbnd1lem2  26970  tghilberti2  27201  btwnconn1lem2  34481  btwnconn1lem3  34482  btwnconn1lem4  34483  athgt  37717  2llnjN  37828  4atlem12b  37872  lncmp  38044  cdlema2N  38053  cdleme21ct  38590  cdleme24  38613  cdleme27a  38628  cdleme28  38634  cdleme42b  38739  cdlemf  38824  dihlsscpre  39495  dihord4  39519  dihord5apre  39523  pellex  40907  jm2.27  41081