Theorem simp1i 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
simp1i	⊢ 𝜑

Proof of Theorem simp1i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp1 1137	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
3	1, 2	ax-mp 5	1 ⊢ 𝜑

Syntax hints:   ∧ w3a 1087

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 1089

This theorem is referenced by:  find  7847  hartogslem2  9460  harwdom  9508  divalglem6  16337  structfn  17095  strleun  17096  oppcbas  17653  rescbas  17765  rescabs  17769  rmodislmod  20893  sratset  21147  srads  21149  tngsca  24601  birthday  26932  divsqrsumf  26959  emcl  26981  lgslem4  27279  lgscllem  27283  lgsdir2lem2  27305  mulog2sumlem1  27513  siilem2  30939  h2hva  31061  h2hsm  31062  elunop2  32100  zlmds  34139  zlmtset  34140  wallispilem3  46422  wallispilem4  46423  prstcbas  49910  cnelsubclem  49959