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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 33926 | . 2 ⊢ (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵)) | |
2 | df-bj-1upl 33936 | . 2 ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴) | |
3 | df-bj-1upl 33936 | . 2 ⊢ ⦅𝐵⦆ = ({∅} × tag 𝐵) | |
4 | 1, 2, 3 | 3eqtr4g 2858 | 1 ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1525 ∅c0 4217 {csn 4478 × cxp 5448 tag bj-ctag 33912 ⦅bj-c1upl 33935 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1781 ax-4 1795 ax-5 1892 ax-6 1951 ax-7 1996 ax-8 2085 ax-9 2093 ax-10 2114 ax-11 2128 ax-12 2143 ax-ext 2771 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-tru 1528 df-ex 1766 df-nf 1770 df-sb 2045 df-clab 2778 df-cleq 2790 df-clel 2865 df-nfc 2937 df-rex 3113 df-v 3442 df-un 3870 df-opab 5031 df-xp 5456 df-bj-sngl 33904 df-bj-tag 33913 df-bj-1upl 33936 |
This theorem is referenced by: bj-1uplth 33945 bj-2upleq 33950 |
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