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  7107  omeu  8213  ntrivcvgmul  15260  tsmsxp  22765  tgqioo  23410  ovolunlem2  24101  plyadd  24809  plymul  24810  coeeu  24817  tghilberti2  26426  nosupbnd1lem2  33211  btwnconn1lem2  33551  btwnconn1lem3  33552  btwnconn1lem4  33553  athgt  36594  2llnjN  36705  4atlem12b  36749  lncmp  36921  cdlema2N  36930  cdleme21ct  37467  cdleme24  37490  cdleme27a  37505  cdleme28  37511  cdleme42b  37616  cdlemf  37701  dihlsscpre  38372  dihord4  38396  dihord5apre  38400  pellex  39439  jm2.27  39612