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Theorem cbvdisjv 4003
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 2329 . 2 𝑦𝐵
2 nfcv 2329 . 2 𝑥𝐶
3 cbvdisjv.1 . 2 (𝑥 = 𝑦𝐵 = 𝐶)
41, 2, 3cbvdisj 4002 1 (Disj 𝑥𝐴 𝐵Disj 𝑦𝐴 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105   = wceq 1363  Disj wdisj 3992
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-eu 2039  df-mo 2040  df-cleq 2180  df-clel 2183  df-nfc 2318  df-rex 2471  df-reu 2472  df-rmo 2473  df-disj 3993
This theorem is referenced by: (None)
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