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Theorem cbvrmo 2933
 Description: Change the bound variable of restricted "at most one" using implicit substitution. (Contributed by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
cbvral.1
cbvral.2
cbvral.3
Assertion
Ref Expression
cbvrmo
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvrmo
StepHypRef Expression
1 cbvral.1 . . . 4
2 cbvral.2 . . . 4
3 cbvral.3 . . . 4
41, 2, 3cbvrex 2931 . . 3
51, 2, 3cbvreu 2932 . . 3
64, 5imbi12i 318 . 2
7 rmo5 2926 . 2
8 rmo5 2926 . 2
96, 7, 83bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wnf 1554  wrex 2708  wreu 2709  wrmo 2710 This theorem is referenced by:  cbvrmov  2937  cbvdisj  4194 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-eu 2287  df-mo 2288  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  df-rmo 2715
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