Theorem simp1i 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
simp1i	⊢ 𝜑

Proof of Theorem simp1i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp1 1136	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
3	1, 2	ax-mp 5	1 ⊢ 𝜑

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:  find  7891  hartogslem2  9557  harwdom  9605  divalglem6  16417  structfn  17175  strleun  17176  oppcbas  17730  rescbas  17842  rescabs  17846  rmodislmod  20887  sratset  21141  srads  21143  tngsca  24584  birthday  26916  divsqrsumf  26943  emcl  26965  lgslem4  27263  lgscllem  27267  lgsdir2lem2  27289  mulog2sumlem1  27497  siilem2  30833  h2hva  30955  h2hsm  30956  elunop2  31994  zlmds  33993  zlmtset  33994  wallispilem3  46096  wallispilem4  46097  prstcbas  49431  cnelsubclem  49480