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  7871  hartogslem2  9496  harwdom  9544  divalglem6  16368  structfn  17126  strleun  17127  oppcbas  17679  rescbas  17791  rescabs  17795  rmodislmod  20836  sratset  21090  srads  21092  tngsca  24533  birthday  26864  divsqrsumf  26891  emcl  26913  lgslem4  27211  lgscllem  27215  lgsdir2lem2  27237  mulog2sumlem1  27445  siilem2  30781  h2hva  30903  h2hsm  30904  elunop2  31942  zlmds  33952  zlmtset  33953  wallispilem3  46065  wallispilem4  46066  prstcbas  49543  cnelsubclem  49592