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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-1upleq | Structured version Visualization version GIF version |
Description: Substitution property for ⦅ − ⦆. (Contributed by BJ, 6-Apr-2019.) |
Ref | Expression |
---|---|
bj-1upleq | ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-xtageq 35272 | . 2 ⊢ (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵)) | |
2 | df-bj-1upl 35282 | . 2 ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴) | |
3 | df-bj-1upl 35282 | . 2 ⊢ ⦅𝐵⦆ = ({∅} × tag 𝐵) | |
4 | 1, 2, 3 | 3eqtr4g 2801 | 1 ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1540 ∅c0 4269 {csn 4573 × cxp 5618 tag bj-ctag 35258 ⦅bj-c1upl 35281 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2714 df-cleq 2728 df-clel 2814 df-ral 3062 df-rex 3071 df-v 3443 df-un 3903 df-opab 5155 df-xp 5626 df-bj-sngl 35250 df-bj-tag 35259 df-bj-1upl 35282 |
This theorem is referenced by: bj-1uplth 35291 bj-2upleq 35296 |
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