Theorem wlimeq1 36480

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 2760	. 2 ⊢ 𝐴 = 𝐴
2		wlimeq12 36479	. 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 36471

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 2147  ax-9 2155  ax-ext 2732

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 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-ral 3077  df-rex 3087  df-rab 3413  df-v 3452  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4280  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4868  df-br 5104  df-opab 5168  df-xp 5661  df-cnv 5663  df-dm 5665  df-rn 5666  df-res 5667  df-ima 5668  df-pred 6301  df-sup 9419  df-inf 9420  df-wlim 36473

This theorem is used by: (None)