Theorem simp3lr 1241

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 767	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1131	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  f1oiso2  7105  omeu  8211  ntrivcvgmul  15258  tsmsxp  22763  tgqioo  23408  ovolunlem2  24099  plyadd  24807  plymul  24808  coeeu  24815  tghilberti2  26424  nosupbnd1lem2  33209  btwnconn1lem2  33549  btwnconn1lem3  33550  btwnconn1lem4  33551  athgt  36607  2llnjN  36718  4atlem12b  36762  lncmp  36934  cdlema2N  36943  cdleme21ct  37480  cdleme24  37503  cdleme27a  37518  cdleme28  37524  cdleme42b  37629  cdlemf  37714  dihlsscpre  38385  dihord4  38409  dihord5apre  38413  pellex  39452  jm2.27  39625