Theorem wlimeq1 36582

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 36581	. 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 1569  WLimcwlim 36573

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  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-ss 3896  df-dif 4047  df-in 4091  df-un 4151  df-nul 4279  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5103  df-opab 5167  df-xp 5656  df-cnv 5658  df-dm 5660  df-rn 5661  df-res 5662  df-ima 5663  df-pred 6304  df-sup 9434  df-inf 9435  df-wlim 36575

This theorem is used by: (None)