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Mirrors > Home > MPE Home > Th. List > Mathboxes > wlimeq1 | Structured version Visualization version GIF version |
Description: Equality theorem for the limit class. (Contributed by Scott Fenton, 15-Jun-2018.) |
Ref | Expression |
---|---|
wlimeq1 | ⊢ (𝑅 = 𝑆 → WLim(𝑅, 𝐴) = WLim(𝑆, 𝐴)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2821 | . 2 ⊢ 𝐴 = 𝐴 | |
2 | wlimeq12 33101 | . 2 ⊢ ((𝑅 = 𝑆 ∧ 𝐴 = 𝐴) → WLim(𝑅, 𝐴) = WLim(𝑆, 𝐴)) | |
3 | 1, 2 | mpan2 689 | 1 ⊢ (𝑅 = 𝑆 → WLim(𝑅, 𝐴) = WLim(𝑆, 𝐴)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1533 WLimcwlim 33093 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ne 3017 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3497 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-nul 4292 df-if 4468 df-sn 4562 df-pr 4564 df-op 4568 df-uni 4833 df-br 5060 df-opab 5122 df-xp 5556 df-cnv 5558 df-dm 5560 df-rn 5561 df-res 5562 df-ima 5563 df-pred 6143 df-sup 8900 df-inf 8901 df-wlim 33095 |
This theorem is referenced by: (None) |
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