Theorem wlimeq1 36352

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 2765	. 2 ⊢ 𝐴 = 𝐴
2		wlimeq12 36351	. 2 ⊢ ((𝑅 = 𝑆 ∧ 𝐴 = 𝐴) → WLim(𝑅, 𝐴) = WLim(𝑆, 𝐴))
3	1, 2	mpan2 704	1 ⊢ (𝑅 = 𝑆 → WLim(𝑅, 𝐴) = WLim(𝑆, 𝐴))

This proof depends on syntax axioms:   → wi 4   = wceq 1570  WLimcwlim 36343

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-ne 2961  df-ral 3082  df-rex 3092  df-rab 3419  df-v 3459  df-dif 3909  df-un 3911  df-in 3913  df-ss 3923  df-nul 4287  df-if 4490  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4875  df-br 5112  df-opab 5176  df-xp 5669  df-cnv 5671  df-dm 5673  df-rn 5674  df-res 5675  df-ima 5676  df-pred 6307  df-sup 9410  df-inf 9411  df-wlim 36345

This theorem is used by: (None)