Theorem simp2i 1140

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp2i	⊢ 𝜓

Proof of Theorem simp2i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp2 1137	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)
3	1, 2	ax-mp 5	1 ⊢ 𝜓

Syntax hints:   ∧ w3a 1086

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 1088

This theorem is referenced by:  hartogslem2  9454  harwdom  9502  divalglem6  16327  strleun  17086  oppcbas  17642  sratset  21105  srads  21107  tngvsca  24550  birthdaylem3  26879  birthday  26880  divsqrsum  26908  harmonicbnd  26930  lgslem4  27227  lgscllem  27231  lgsdir2lem2  27253  mulog2sum  27464  vmalogdivsum2  27465  siilem2  30814  h2hva  30936  h2hsm  30937  hhssabloi  31224  elunop2  31975  1fldgenq  33271  zlmds  33928  zlmtset  33929  wallispilem3  46049  wallispilem4  46050  prstcbas  49540  cnelsubclem  49589