Theorem simp1i 1137

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 1134	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
3	1, 2	ax-mp 5	1 ⊢ 𝜑

Syntax hints:   ∧ w3a 1085

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 396  df-3an 1087

This theorem is referenced by:  find  7717  findOLD  7718  hartogslem2  9232  harwdom  9280  divalglem6  16035  structfn  16785  strleun  16786  oppcbas  17345  rescbas  17458  rmodislmod  20106  rmodislmodOLD  20107  sratset  20365  srads  20368  tngsca  23711  birthday  26009  divsqrsumf  26035  emcl  26057  lgslem4  26353  lgscllem  26357  lgsdir2lem2  26379  mulog2sumlem1  26587  siilem2  29115  h2hva  29237  h2hsm  29238  elunop2  30276  wallispilem3  43498  wallispilem4  43499  prstcbas  46236