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Theorem cbvdisjv 4663
Description: Change bound variables in a disjoint collection. (Contributed by Mario Carneiro, 11-Dec-2016.)
Hypothesis
Ref Expression
cbvdisjv.1 (𝑥 = 𝑦𝐵 = 𝐶)
Assertion
Ref Expression
cbvdisjv (Disj 𝑥𝐴 𝐵Disj 𝑦𝐴 𝐶)
Distinct variable groups:   𝑥,𝑦,𝐴   𝑦,𝐵   𝑥,𝐶
Allowed substitution hints:   𝐵(𝑥)   𝐶(𝑦)

Proof of Theorem cbvdisjv
StepHypRef Expression
1 nfcv 2793 . 2 𝑦𝐵
2 nfcv 2793 . 2 𝑥𝐶
3 cbvdisjv.1 . 2 (𝑥 = 𝑦𝐵 = 𝐶)
41, 2, 3cbvdisj 4662 1 (Disj 𝑥𝐴 𝐵Disj 𝑦𝐴 𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1523  Disj wdisj 4652
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rex 2947  df-reu 2948  df-rmo 2949  df-disj 4653
This theorem is referenced by:  uniioombllem4  23400  hashunif  29690  totprob  30617  disjrnmpt2  39689  ismeannd  41002  psmeasure  41006  volmea  41009  meaiuninclem  41015  caratheodorylem1  41061  caratheodory  41063
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