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Theorem cbvrexcsf 3314
 Description: A more general version of cbvrexf 2929 that has no distinct variable restrictions. Changes bound variables using implicit substitution. (Contributed by Andrew Salmon, 13-Jul-2011.) (Proof shortened by Mario Carneiro, 7-Dec-2014.)
Hypotheses
Ref Expression
cbvralcsf.1
cbvralcsf.2
cbvralcsf.3
cbvralcsf.4
cbvralcsf.5
cbvralcsf.6
Assertion
Ref Expression
cbvrexcsf

Proof of Theorem cbvrexcsf
StepHypRef Expression
1 cbvralcsf.1 . . . 4
2 cbvralcsf.2 . . . 4
3 cbvralcsf.3 . . . . 5
43nfn 1812 . . . 4
5 cbvralcsf.4 . . . . 5
65nfn 1812 . . . 4
7 cbvralcsf.5 . . . 4
8 cbvralcsf.6 . . . . 5
98notbid 287 . . . 4
101, 2, 4, 6, 7, 9cbvralcsf 3313 . . 3
1110notbii 289 . 2
12 dfrex2 2720 . 2
13 dfrex2 2720 . 2
1411, 12, 133bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wnf 1554   wceq 1653  wnfc 2561  wral 2707  wrex 2708 This theorem is referenced by:  cbvrexv2  3318 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-sbc 3164  df-csb 3254
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