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Theorem bj-xtageq 32951
Description: The products of a given class and the tagging of either of two equal classes are equal. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-xtageq (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))

Proof of Theorem bj-xtageq
StepHypRef Expression
1 bj-tageq 32939 . 2 (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
21xpeq2d 5129 1 (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1481   × cxp 5102  tag bj-ctag 32937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rex 2915  df-v 3197  df-un 3572  df-opab 4704  df-xp 5110  df-bj-sngl 32929  df-bj-tag 32938
This theorem is referenced by:  bj-1upleq  32962  bj-2upleq  32975
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