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Mirrors > Home > MPE Home > Th. List > Mathboxes > wlimeq2 | Structured version Visualization version GIF version |
Description: Equality theorem for the limit class. (Contributed by Scott Fenton, 15-Jun-2018.) |
Ref | Expression |
---|---|
wlimeq2 | ⊢ (𝐴 = 𝐵 → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2728 | . 2 ⊢ 𝑅 = 𝑅 | |
2 | wlimeq12 35410 | . 2 ⊢ ((𝑅 = 𝑅 ∧ 𝐴 = 𝐵) → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵)) | |
3 | 1, 2 | mpan 689 | 1 ⊢ (𝐴 = 𝐵 → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1534 WLimcwlim 35402 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-clel 2806 df-ne 2937 df-ral 3058 df-rex 3067 df-rab 3429 df-v 3472 df-dif 3948 df-un 3950 df-in 3952 df-ss 3962 df-nul 4320 df-if 4526 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4905 df-br 5144 df-opab 5206 df-xp 5679 df-cnv 5681 df-dm 5683 df-rn 5684 df-res 5685 df-ima 5686 df-pred 6300 df-sup 9460 df-inf 9461 df-wlim 35404 |
This theorem is referenced by: (None) |
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