Theorem wlimeq2 35326

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

Step	Hyp	Ref	Expression
1		eqid 2726	. 2 ⊢ 𝑅 = 𝑅
2		wlimeq12 35324	. 2 ⊢ ((𝑅 = 𝑅 ∧ 𝐴 = 𝐵) → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))
3	1, 2	mpan 687	1 ⊢ (𝐴 = 𝐵 → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))

Syntax hints:   → wi 4   = wceq 1533  WLimcwlim 35316

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ne 2935  df-ral 3056  df-rex 3065  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-opab 5204  df-xp 5675  df-cnv 5677  df-dm 5679  df-rn 5680  df-res 5681  df-ima 5682  df-pred 6293  df-sup 9436  df-inf 9437  df-wlim 35318

This theorem is referenced by: (None)