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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 34291 | . 2 ⊢ (𝐴 = 𝐵 → tag 𝐴 = tag 𝐵) | |
2 | 1 | xpeq2d 5585 | 1 ⊢ (𝐴 = 𝐵 → (𝐶 × tag 𝐴) = (𝐶 × tag 𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 × cxp 5553 tag bj-ctag 34289 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rex 3144 df-v 3496 df-un 3941 df-opab 5129 df-xp 5561 df-bj-sngl 34281 df-bj-tag 34290 |
This theorem is referenced by: bj-1upleq 34314 bj-2upleq 34327 |
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