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Theorem sbiedh 1711
 Description: Conversion of implicit substitution to explicit substitution (deduction version of sbieh 1714). New proofs should use sbied 1712 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 1690 . . . 4
2 sbiedh.1 . . . . 5
3 sbiedh.3 . . . . . . 7
4 bi1 116 . . . . . . 7
53, 4syl6 33 . . . . . 6
65impd 251 . . . . 5
72, 6eximdh 1543 . . . 4
81, 7syl5 32 . . 3
9 sbiedh.2 . . . 4
102, 919.9hd 1593 . . 3
118, 10syld 44 . 2
12 bi2 128 . . . . . . 7
133, 12syl6 33 . . . . . 6
1413com23 77 . . . . 5
152, 14alimdh 1397 . . . 4
16 sb2 1691 . . . 4
1715, 16syl6 33 . . 3
189, 17syld 44 . 2
1911, 18impbid 127 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283  wex 1422  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-i9 1464  ax-ial 1468 This theorem depends on definitions:  df-bi 115  df-sb 1687 This theorem is referenced by:  sbied  1712  sbieh  1714  sbcomxyyz  1888
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