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Theorem simp1i 1063
Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)
Hypothesis
Ref Expression
3simp1i.1 (𝜑𝜓𝜒)
Assertion
Ref Expression
simp1i 𝜑

Proof of Theorem simp1i
StepHypRef Expression
1 3simp1i.1 . 2 (𝜑𝜓𝜒)
2 simp1 1054 . 2 ((𝜑𝜓𝜒) → 𝜑)
31, 2ax-mp 5 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  w3a 1031
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 196  df-an 385  df-3an 1033
This theorem is referenced by:  find  6983  hartogslem2  8331  harwdom  8378  divalglem6  14959  structfn  15708  strleun  15799  birthday  24481  divsqrsumf  24507  emcl  24529  lgslem4  24825  lgscllem  24829  lgsdir2lem2  24851  mulog2sumlem1  25023  siilem2  27091  h2hva  27215  h2hsm  27216  elunop2  28256  wallispilem3  38960  wallispilem4  38961
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