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 1088

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 398  df-3an 1090

This theorem is referenced by:  hartogslem2  9535  harwdom  9583  divalglem6  16338  strleun  17087  oppcbas  17660  sratset  20796  srads  20799  tngvsca  24152  birthdaylem3  26448  birthday  26449  divsqrsum  26476  harmonicbnd  26498  lgslem4  26793  lgscllem  26797  lgsdir2lem2  26819  mulog2sum  27030  vmalogdivsum2  27031  siilem2  30093  h2hva  30215  h2hsm  30216  hhssabloi  30503  elunop2  31254  1fldgenq  32401  zlmds  32931  zlmtset  32933  wallispilem3  44770  wallispilem4  44771  prstcbas  47641