Theorem simp2i 1139

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 1136	. 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 206  df-an 396  df-3an 1088

This theorem is referenced by:  hartogslem2  9544  harwdom  9592  divalglem6  16348  strleun  17097  oppcbas  17670  sratset  21037  srads  21040  tngvsca  24480  birthdaylem3  26799  birthday  26800  divsqrsum  26827  harmonicbnd  26849  lgslem4  27146  lgscllem  27150  lgsdir2lem2  27172  mulog2sum  27383  vmalogdivsum2  27384  siilem2  30538  h2hva  30660  h2hsm  30661  hhssabloi  30948  elunop2  31699  1fldgenq  32848  zlmds  33406  zlmtset  33408  wallispilem3  45242  wallispilem4  45243  prstcbas  47849