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  9496  harwdom  9544  divalglem6  16368  strleun  17127  oppcbas  17679  sratset  21090  srads  21092  tngvsca  24534  birthdaylem3  26863  birthday  26864  divsqrsum  26892  harmonicbnd  26914  lgslem4  27211  lgscllem  27215  lgsdir2lem2  27237  mulog2sum  27448  vmalogdivsum2  27449  siilem2  30781  h2hva  30903  h2hsm  30904  hhssabloi  31191  elunop2  31942  1fldgenq  33272  zlmds  33952  zlmtset  33953  wallispilem3  46065  wallispilem4  46066  prstcbas  49543  cnelsubclem  49592