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Theorem cbvmptvOLD 5223
Description: Obsolete version of cbvmptv 5222 as of 17-Nov-2024. (Contributed by Mario Carneiro, 19-Feb-2013.) Add disjoint variable condition to avoid ax-13 2371. See cbvmptvg 5224 for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 17-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
cbvmptvOLD.1 (𝑥 = 𝑦𝐵 = 𝐶)
Assertion
Ref Expression
cbvmptvOLD (𝑥𝐴𝐵) = (𝑦𝐴𝐶)
Distinct variable groups:   𝑥,𝐴,𝑦   𝑦,𝐵   𝑥,𝐶
Allowed substitution hints:   𝐵(𝑥)   𝐶(𝑦)

Proof of Theorem cbvmptvOLD
StepHypRef Expression
1 nfcv 2904 . 2 𝑦𝐵
2 nfcv 2904 . 2 𝑥𝐶
3 cbvmptvOLD.1 . 2 (𝑥 = 𝑦𝐵 = 𝐶)
41, 2, 3cbvmpt 5220 1 (𝑥𝐴𝐵) = (𝑦𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  cmpt 5192
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-opab 5172  df-mpt 5193
This theorem is referenced by: (None)
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