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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-xtageq | Structured version Visualization version GIF version |
Description: The products of a given class and the tagging of either of two equal classes are equal. (Contributed by BJ, 6-Apr-2019.) |
Ref | Expression |
---|---|
bj-xtageq | ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-tageq 34852 | . 2 ⊢ (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵) | |
2 | 1 | xpeq2d 5566 | 1 ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1543 × cxp 5534 tag bj-ctag 34850 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2018 ax-8 2114 ax-9 2122 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-ex 1788 df-sb 2073 df-clab 2715 df-cleq 2728 df-clel 2809 df-ral 3056 df-rex 3057 df-v 3400 df-un 3858 df-opab 5102 df-xp 5542 df-bj-sngl 34842 df-bj-tag 34851 |
This theorem is referenced by: bj-1upleq 34875 bj-2upleq 34888 |
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