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Theorem cbvrexcsf 3199
Description: A more general version of cbvrexf 2830 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  F/_
cbvralcsf.2  F/_
cbvralcsf.3  F/
cbvralcsf.4  F/
cbvralcsf.5
cbvralcsf.6
Assertion
Ref Expression
cbvrexcsf

Proof of Theorem cbvrexcsf
StepHypRef Expression
1 cbvralcsf.1 . . . 4  F/_
2 cbvralcsf.2 . . . 4  F/_
3 cbvralcsf.3 . . . . 5  F/
43nfn 1793 . . . 4  F/
5 cbvralcsf.4 . . . . 5  F/
65nfn 1793 . . . 4  F/
7 cbvralcsf.5 . . . 4
8 cbvralcsf.6 . . . . 5
98notbid 285 . . . 4
101, 2, 4, 6, 7, 9cbvralcsf 3198 . . 3
1110notbii 287 . 2
12 dfrex2 2627 . 2
13 dfrex2 2627 . 2
1411, 12, 133bitr4i 268 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   F/wnf 1544   wceq 1642   F/_wnfc 2476  wral 2614  wrex 2615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-sbc 3047  df-csb 3137
This theorem is referenced by:  cbvrexv2  3203
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