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 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:  find  7887  findOLD  7888  hartogslem2  9538  harwdom  9586  divalglem6  16341  structfn  17089  strleun  17090  oppcbas  17663  rescbas  17776  rescabs  17782  rmodislmod  20540  rmodislmodOLD  20541  sratset  20803  srads  20806  tngsca  24158  birthday  26459  divsqrsumf  26485  emcl  26507  lgslem4  26803  lgscllem  26807  lgsdir2lem2  26829  mulog2sumlem1  27037  siilem2  30105  h2hva  30227  h2hsm  30228  elunop2  31266  zlmds  32942  zlmtset  32944  wallispilem3  44783  wallispilem4  44784  prstcbas  47687