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Theorem wlimeq2 35412
Description: Equality theorem for the limit class. (Contributed by Scott Fenton, 15-Jun-2018.)
Assertion
Ref Expression
wlimeq2 (𝐴 = 𝐵 → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))

Proof of Theorem wlimeq2
StepHypRef Expression
1 eqid 2728 . 2 𝑅 = 𝑅
2 wlimeq12 35410 . 2 ((𝑅 = 𝑅𝐴 = 𝐵) → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))
31, 2mpan 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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