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Theorem 3anim1i 1153
Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)
Hypothesis
Ref Expression
3animi.1 (𝜑𝜓)
Assertion
Ref Expression
3anim1i ((𝜑𝜒𝜃) → (𝜓𝜒𝜃))

Proof of Theorem 3anim1i
StepHypRef Expression
1 3animi.1 . 2 (𝜑𝜓)
2 id 22 . 2 (𝜒𝜒)
3 id 22 . 2 (𝜃𝜃)
41, 2, 33anim123i 1152 1 ((𝜑𝜒𝜃) → (𝜓𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  syl3an1  1164  syl3anl1  1414  syl3anr1  1418  fnsuppres  8216  dif1en  9200  elfiun  9470  elioc2  13450  elico2  13451  elicc2  13452  dvdsleabs2  16349  subrngringnsg  20553  cphipval  25277  spthonpthon  29771  uhgrwkspth  29775  usgr2wlkspth  29779  upgriseupth  30226  cm2j  31639  bnj544  34908  btwnconn1lem4  36091  relowlssretop  37364  dalem53  39727  dalem54  39728  paddasslem14  39835  mzpcong  42984  itscnhlc0xyqsol  48686
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