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Theorem spsbim 1721
Description: Specialization of implication. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 21-Jan-2018.)
Assertion
Ref Expression
spsbim

Proof of Theorem spsbim
StepHypRef Expression
1 imim2 49 . . . 4
21sps 1427 . . 3
3 id 19 . . . . . 6
43anim2d 320 . . . . 5
54alimi 1341 . . . 4
6 exim 1487 . . . 4
75, 6syl 14 . . 3
82, 7anim12d 318 . 2
9 df-sb 1643 . 2
10 df-sb 1643 . 2
118, 9, 103imtr4g 194 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240  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:  spsbbi  1722  hbsb4t  1886  moim  1961
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