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Theorem sbiedh 1667
Description: Conversion of implicit substitution to explicit substitution (deduction version of sbieh 1670). New proofs should use sbied 1668 instead. (Contributed by NM, 30-Jun-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
sbiedh.1
sbiedh.2
sbiedh.3
Assertion
Ref Expression
sbiedh

Proof of Theorem sbiedh
StepHypRef Expression
1 sb1 1646 . . . 4
2 sbiedh.1 . . . . 5
3 sbiedh.3 . . . . . . 7
4 bi1 111 . . . . . . 7
53, 4syl6 29 . . . . . 6
65impd 242 . . . . 5
72, 6eximdh 1499 . . . 4
81, 7syl5 28 . . 3
9 sbiedh.2 . . . 4
102, 919.9hd 1549 . . 3
118, 10syld 40 . 2
12 bi2 121 . . . . . . 7
133, 12syl6 29 . . . . . 6
1413com23 72 . . . . 5
152, 14alimdh 1353 . . . 4
16 sb2 1647 . . . 4
1715, 16syl6 29 . . 3
189, 17syld 40 . 2
1911, 18impbid 120 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  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-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbied  1668  sbieh  1670  sbcomxyyz  1843
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