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  7917  hartogslem2  9583  harwdom  9631  divalglem6  16435  structfn  17193  strleun  17194  oppcbas  17761  rescbas  17873  rescabs  17877  rmodislmod  20928  sratset  21188  srads  21191  tngsca  24662  birthday  26997  divsqrsumf  27024  emcl  27046  lgslem4  27344  lgscllem  27348  lgsdir2lem2  27370  mulog2sumlem1  27578  siilem2  30871  h2hva  30993  h2hsm  30994  elunop2  32032  zlmds  33961  zlmtset  33963  wallispilem3  46082  wallispilem4  46083  prstcbas  49156