![]() |
Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
|
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 2797 | . 2 ⊢ 𝑅 = 𝑅 | |
2 | wlimeq12 32717 | . 2 ⊢ ((𝑅 = 𝑅 ∧ 𝐴 = 𝐵) → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵)) | |
3 | 1, 2 | mpan 686 | 1 ⊢ (𝐴 = 𝐵 → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1525 WLimcwlim 32709 |
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-3an 1082 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-ne 2987 df-ral 3112 df-rex 3113 df-rab 3116 df-v 3442 df-dif 3868 df-un 3870 df-in 3872 df-ss 3880 df-nul 4218 df-if 4388 df-sn 4479 df-pr 4481 df-op 4485 df-uni 4752 df-br 4969 df-opab 5031 df-xp 5456 df-cnv 5458 df-dm 5460 df-rn 5461 df-res 5462 df-ima 5463 df-pred 6030 df-sup 8759 df-inf 8760 df-wlim 32711 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |