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Theorem sbimi 1644
Description: Infer substitution into antecedent and consequent of an implication. (Contributed by NM, 25-Jun-1998.)
Hypothesis
Ref Expression
sbimi.1
Assertion
Ref Expression
sbimi

Proof of Theorem sbimi
StepHypRef Expression
1 sbimi.1 . . . 4
21imim2i 12 . . 3
31anim2i 324 . . . 4
43eximi 1488 . . 3
52, 4anim12i 321 . 2
6 df-sb 1643 . 2
7 df-sb 1643 . 2
85, 6, 73imtr4i 190 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wex 1378  wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbbii  1645  sb6f  1681  hbsb3  1686  sbidm  1728  sbco  1839  sbcocom  1841  elsb3  1849  elsb4  1850  sbalyz  1872  hbsb4t  1886  moimv  1963  oprcl  3564  peano1  4260  peano2  4261
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