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Theorem sbimi 1647
 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 1491 . . 3
52, 4anim12i 321 . 2
6 df-sb 1646 . 2
7 df-sb 1646 . 2
85, 6, 73imtr4i 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wex 1381  wsb 1645 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-sb 1646 This theorem is referenced by:  sbbii  1648  sb6f  1684  hbsb3  1689  sbidm  1731  sbco  1842  sbcocom  1844  elsb3  1852  elsb4  1853  sbalyz  1875  hbsb4t  1889  moimv  1966  oprcl  3573  peano1  4317  peano2  4318
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