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 769	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1136	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  f1oiso2  7372  omeu  8623  ntrivcvgmul  15938  tsmsxp  24163  tgqioo  24821  ovolunlem2  25533  plyadd  26256  plymul  26257  coeeu  26264  nosupbnd1lem2  27754  noinfbnd1lem2  27769  tghilberti2  28646  btwnconn1lem2  36089  btwnconn1lem3  36090  btwnconn1lem4  36091  athgt  39458  2llnjN  39569  4atlem12b  39613  lncmp  39785  cdlema2N  39794  cdleme21ct  40331  cdleme24  40354  cdleme27a  40369  cdleme28  40375  cdleme42b  40480  cdlemf  40565  dihlsscpre  41236  dihord4  41260  dihord5apre  41264  pellex  42846  jm2.27  43020