Theorem wlimeq1 33102

Description: Equality theorem for the limit class. (Contributed by Scott Fenton, 15-Jun-2018.)

Assertion

Ref	Expression
wlimeq1	⊢ (𝑅 = 𝑆 → WLim(𝑅, 𝐴) = WLim(𝑆, 𝐴))

Proof of Theorem wlimeq1

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))

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)