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 395   ∧ 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 396  df-3an 1087

This theorem is referenced by:  f1oiso2  7203  omeu  8378  ntrivcvgmul  15542  tsmsxp  23214  tgqioo  23869  ovolunlem2  24567  plyadd  25283  plymul  25284  coeeu  25291  tghilberti2  26903  nosupbnd1lem2  33839  noinfbnd1lem2  33854  btwnconn1lem2  34317  btwnconn1lem3  34318  btwnconn1lem4  34319  athgt  37397  2llnjN  37508  4atlem12b  37552  lncmp  37724  cdlema2N  37733  cdleme21ct  38270  cdleme24  38293  cdleme27a  38308  cdleme28  38314  cdleme42b  38419  cdlemf  38504  dihlsscpre  39175  dihord4  39199  dihord5apre  39203  pellex  40573  jm2.27  40746