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Theorem bj-xtageq 34419
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 34407 . 2 (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
21xpeq2d 5553 1 (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538   × cxp 5521  tag bj-ctag 34405
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-12 2176  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-rex 3115  df-v 3446  df-un 3889  df-opab 5096  df-xp 5529  df-bj-sngl 34397  df-bj-tag 34406
This theorem is referenced by:  bj-1upleq  34430  bj-2upleq  34443
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