 Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-xtageq Structured version   Visualization version   GIF version

Theorem bj-xtageq 33851
 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 33839 . 2 (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
21xpeq2d 5434 1 (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1508   × cxp 5402  tag bj-ctag 33837 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773  ax-5 1870  ax-6 1929  ax-7 1966  ax-8 2053  ax-9 2060  ax-10 2080  ax-11 2094  ax-12 2107  ax-ext 2745 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 835  df-tru 1511  df-ex 1744  df-nf 1748  df-sb 2017  df-clab 2754  df-cleq 2766  df-clel 2841  df-nfc 2913  df-rex 3089  df-v 3412  df-un 3829  df-opab 4989  df-xp 5410  df-bj-sngl 33829  df-bj-tag 33838 This theorem is referenced by:  bj-1upleq  33862  bj-2upleq  33875
 Copyright terms: Public domain W3C validator