Theorem simp2i 1137

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 1134	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)
3	1, 2	ax-mp 5	1 ⊢ 𝜓

Syntax hints:   ∧ w3a 1084

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 395  df-3an 1086

This theorem is referenced by:  hartogslem2  9568  harwdom  9616  divalglem6  16378  strleun  17129  oppcbas  17702  sratset  21086  srads  21089  tngvsca  24604  birthdaylem3  26930  birthday  26931  divsqrsum  26959  harmonicbnd  26981  lgslem4  27278  lgscllem  27282  lgsdir2lem2  27304  mulog2sum  27515  vmalogdivsum2  27516  siilem2  30734  h2hva  30856  h2hsm  30857  hhssabloi  31144  elunop2  31895  1fldgenq  33108  zlmds  33694  zlmtset  33696  wallispilem3  45593  wallispilem4  45594  prstcbas  48259