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Theorem cbvrmo 3083
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:   ,   ,

Proof of Theorem cbvrmo
StepHypRef Expression
1 cbvral.1 . . . 4
2 cbvral.2 . . . 4
3 cbvral.3 . . . 4
41, 2, 3cbvrex 3081 . . 3
51, 2, 3cbvreu 3082 . . 3
64, 5imbi12i 326 . 2
7 rmo5 3076 . 2
8 rmo5 3076 . 2
96, 7, 83bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  F/wnf 1616  E.wrex 2808  E!wreu 2809  E*wrmo 2810
This theorem is referenced by:  cbvrmov  3087  cbvdisj  4432
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815
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