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  9557  harwdom  9605  divalglem6  16417  strleun  17176  oppcbas  17730  sratset  21141  srads  21143  tngvsca  24585  birthdaylem3  26915  birthday  26916  divsqrsum  26944  harmonicbnd  26966  lgslem4  27263  lgscllem  27267  lgsdir2lem2  27289  mulog2sum  27500  vmalogdivsum2  27501  siilem2  30833  h2hva  30955  h2hsm  30956  hhssabloi  31243  elunop2  31994  1fldgenq  33316  zlmds  33993  zlmtset  33994  wallispilem3  46096  wallispilem4  46097  prstcbas  49431  cnelsubclem  49480