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Theorem cbvab 2551
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by Andrew Salmon, 11-Jul-2011.)
Hypotheses
Ref Expression
cbvab.1
cbvab.2
cbvab.3
Assertion
Ref Expression
cbvab

Proof of Theorem cbvab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvab.2 . . . . 5
21nfsb 2148 . . . 4
3 cbvab.1 . . . . . 6
4 cbvab.3 . . . . . . . 8
54equcoms 1732 . . . . . . 7
65bicomd 201 . . . . . 6
73, 6sbie 2098 . . . . 5
8 sbequ 2064 . . . . 5
97, 8syl5bbr 259 . . . 4
102, 9sbie 2098 . . 3
11 df-clab 2420 . . 3
12 df-clab 2420 . . 3
1310, 11, 123bitr4i 277 . 2
1413eqriv 2430 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1362  wnf 1592  wsb 1699   wcel 1755  cab 2419 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1594  ax-4 1605  ax-5 1669  ax-6 1707  ax-7 1727  ax-10 1774  ax-11 1779  ax-12 1791  ax-13 1942  ax-ext 2414 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1590  df-nf 1593  df-sb 1700  df-clab 2420  df-cleq 2426 This theorem is referenced by:  cbvabv  2552  cbvrab  2960  cbvsbc  3203  cbvrabcsf  3310  rabsnifsb  3931  dfdmf  5020  dfrnf  5065  funfv2f  5748  abrexex2g  6543  abrexex2  6547  ptrest  28266  rabasiun  30073  bnj873  31616
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