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Theorem sbralie 2546
 Description: Implicit to explicit substitution that swaps variables in a quantified expression. (Contributed by NM, 5-Sep-2004.)
Hypothesis
Ref Expression
sbralie.1
Assertion
Ref Expression
sbralie
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbralie
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvralsv 2544 . . . 4
21sbbii 1648 . . 3
3 nfv 1421 . . . 4
4 raleq 2505 . . . 4
53, 4sbie 1674 . . 3
62, 5bitri 173 . 2
7 cbvralsv 2544 . . 3
8 nfv 1421 . . . . . 6
98sbco2 1839 . . . . 5
10 nfv 1421 . . . . . 6
11 sbralie.1 . . . . . 6
1210, 11sbie 1674 . . . . 5
139, 12bitri 173 . . . 4
1413ralbii 2330 . . 3
157, 14bitri 173 . 2
166, 15bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wsb 1645  wral 2306 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311 This theorem is referenced by: (None)
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