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Theorem cbvdisjv 3988
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 2319 . 2 𝑦𝐵
2 nfcv 2319 . 2 𝑥𝐶
3 cbvdisjv.1 . 2 (𝑥 = 𝑦𝐵 = 𝐶)
41, 2, 3cbvdisj 3987 1 (Disj 𝑥𝐴 𝐵Disj 𝑦𝐴 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105   = wceq 1353  Disj wdisj 3977
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-reu 2462  df-rmo 2463  df-disj 3978
This theorem is referenced by: (None)
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