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Theorem sbralie 2937
 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 2935 . . . 4
21sbbii 1665 . . 3
3 nfv 1629 . . . 4
4 raleq 2896 . . . 4
53, 4sbie 2122 . . 3
62, 5bitri 241 . 2
7 cbvralsv 2935 . . 3
8 nfv 1629 . . . . . 6
98sbco2 2161 . . . . 5
10 nfv 1629 . . . . . 6
11 sbralie.1 . . . . . 6
1210, 11sbie 2122 . . . . 5
139, 12bitri 241 . . . 4
1413ralbii 2721 . . 3
157, 14bitri 241 . 2
166, 15bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wsb 1658  wral 2697 This theorem is referenced by:  tfinds2  4835 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702
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