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Theorem bj-tageq 36977
Description: Substitution property for tag. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-tageq (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)

Proof of Theorem bj-tageq
StepHypRef Expression
1 bj-sngleq 36968 . . 3 (𝐴 = 𝐵 → sngl 𝐴 = sngl 𝐵)
21uneq1d 4167 . 2 (𝐴 = 𝐵 → (sngl 𝐴 ∪ {∅}) = (sngl 𝐵 ∪ {∅}))
3 df-bj-tag 36976 . 2 tag 𝐴 = (sngl 𝐴 ∪ {∅})
4 df-bj-tag 36976 . 2 tag 𝐵 = (sngl 𝐵 ∪ {∅})
52, 3, 43eqtr4g 2802 1 (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  cun 3949  c0 4333  {csn 4626  sngl bj-csngl 36966  tag bj-ctag 36975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rex 3071  df-v 3482  df-un 3956  df-bj-sngl 36967  df-bj-tag 36976
This theorem is referenced by:  bj-xtageq  36989
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