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Theorem bj-xtageq 36990
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 36978 . 2 (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
21xpeq2d 5714 1 (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539   × cxp 5682  tag bj-ctag 36976
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rex 3070  df-v 3481  df-un 3955  df-opab 5205  df-xp 5690  df-bj-sngl 36968  df-bj-tag 36977
This theorem is referenced by:  bj-1upleq  37001  bj-2upleq  37014
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