Theorem simp3lr 1225

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 756	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant3 1115	1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 387   ∧ w3a 1068

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 199  df-an 388  df-3an 1070

This theorem is referenced by:  f1oiso2  6928  omeu  8012  ntrivcvgmul  15118  tsmsxp  22466  tgqioo  23111  ovolunlem2  23802  plyadd  24510  plymul  24511  coeeu  24518  tghilberti2  26126  nosupbnd1lem2  32727  btwnconn1lem2  33067  btwnconn1lem3  33068  btwnconn1lem4  33069  athgt  36034  2llnjN  36145  4atlem12b  36189  lncmp  36361  cdlema2N  36370  cdleme21ct  36907  cdleme24  36930  cdleme27a  36945  cdleme28  36951  cdleme42b  37056  cdlemf  37141  dihlsscpre  37812  dihord4  37836  dihord5apre  37840  pellex  38825  jm2.27  38998