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  7835  hartogslem2  9454  harwdom  9502  divalglem6  16327  structfn  17085  strleun  17086  oppcbas  17642  rescbas  17754  rescabs  17758  rmodislmod  20851  sratset  21105  srads  21107  tngsca  24549  birthday  26880  divsqrsumf  26907  emcl  26929  lgslem4  27227  lgscllem  27231  lgsdir2lem2  27253  mulog2sumlem1  27461  siilem2  30814  h2hva  30936  h2hsm  30937  elunop2  31975  zlmds  33928  zlmtset  33929  wallispilem3  46049  wallispilem4  46050  prstcbas  49540  cnelsubclem  49589