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Theorem cbvrmo 2526
Description: Change the bound variable of restricted "at most one" using implicit substitution. (Contributed by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
cbvral.1  F/
cbvral.2  F/
cbvral.3
Assertion
Ref Expression
cbvrmo
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvrmo
StepHypRef Expression
1 cbvral.1 . . . 4  F/
2 cbvral.2 . . . 4  F/
3 cbvral.3 . . . 4
41, 2, 3cbvrex 2524 . . 3
51, 2, 3cbvreu 2525 . . 3
64, 5imbi12i 228 . 2
7 rmo5 2519 . 2
8 rmo5 2519 . 2
96, 7, 83bitr4i 201 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   F/wnf 1346  wrex 2301  wreu 2302  wrmo 2303
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-reu 2307  df-rmo 2308
This theorem is referenced by:  cbvrmov  2530  cbvdisj  3746
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