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  9583  harwdom  9631  divalglem6  16435  strleun  17194  oppcbas  17761  sratset  21188  srads  21191  tngvsca  24664  birthdaylem3  26996  birthday  26997  divsqrsum  27025  harmonicbnd  27047  lgslem4  27344  lgscllem  27348  lgsdir2lem2  27370  mulog2sum  27581  vmalogdivsum2  27582  siilem2  30871  h2hva  30993  h2hsm  30994  hhssabloi  31281  elunop2  32032  1fldgenq  33324  zlmds  33961  zlmtset  33963  wallispilem3  46082  wallispilem4  46083  prstcbas  49156