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Theorem bj-xtageq 32169
 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 32157 . 2 (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
21xpeq2d 5063 1 (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   × cxp 5036  tag bj-ctag 32155 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-v 3175  df-un 3545  df-opab 4644  df-xp 5044  df-bj-sngl 32147  df-bj-tag 32156 This theorem is referenced by:  bj-1upleq  32180  bj-2upleq  32193
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