Theorem simp2i 1141

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 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)
3	1, 2	ax-mp 5	1 ⊢ 𝜓

Syntax hints:   ∧ 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:  hartogslem2  9458  harwdom  9506  divalglem6  16367  strleun  17127  oppcbas  17684  sratset  21178  srads  21180  tngvsca  24611  birthdaylem3  26917  birthday  26918  divsqrsum  26945  harmonicbnd  26967  lgslem4  27263  lgscllem  27267  lgsdir2lem2  27289  mulog2sum  27500  vmalogdivsum2  27501  siilem2  30923  h2hva  31045  h2hsm  31046  hhssabloi  31333  elunop2  32084  1fldgenq  33383  zlmds  34106  zlmtset  34107  wallispilem3  46495  wallispilem4  46496  prstcbas  50029  cnelsubclem  50078