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  7846  hartogslem2  9458  harwdom  9506  divalglem6  16367  structfn  17126  strleun  17127  oppcbas  17684  rescbas  17796  rescabs  17800  rmodislmod  20925  sratset  21178  srads  21180  tngsca  24610  birthday  26918  divsqrsumf  26944  emcl  26966  lgslem4  27263  lgscllem  27267  lgsdir2lem2  27289  mulog2sumlem1  27497  siilem2  30923  h2hva  31045  h2hsm  31046  elunop2  32084  zlmds  34106  zlmtset  34107  wallispilem3  46495  wallispilem4  46496  prstcbas  50029  cnelsubclem  50078