Theorem simp3lr 1243

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 765	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1133	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1085

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 395  df-3an 1087

This theorem is referenced by:  f1oiso2  7351  omeu  8587  ntrivcvgmul  15852  tsmsxp  23879  tgqioo  24536  ovolunlem2  25247  plyadd  25966  plymul  25967  coeeu  25974  nosupbnd1lem2  27448  noinfbnd1lem2  27463  tghilberti2  28156  btwnconn1lem2  35364  btwnconn1lem3  35365  btwnconn1lem4  35366  athgt  38630  2llnjN  38741  4atlem12b  38785  lncmp  38957  cdlema2N  38966  cdleme21ct  39503  cdleme24  39526  cdleme27a  39541  cdleme28  39547  cdleme42b  39652  cdlemf  39737  dihlsscpre  40408  dihord4  40432  dihord5apre  40436  pellex  41875  jm2.27  42049