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Theorem wlimeq2 32719
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 2797 . 2 𝑅 = 𝑅
2 wlimeq12 32717 . 2 ((𝑅 = 𝑅𝐴 = 𝐵) → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))
31, 2mpan 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)
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