Theorem wlimeq2 33495

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 2736	. 2 ⊢ 𝑅 = 𝑅
2		wlimeq12 33493	. 2 ⊢ ((𝑅 = 𝑅 ∧ 𝐴 = 𝐵) → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))
3	1, 2	mpan 690	1 ⊢ (𝐴 = 𝐵 → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))

Syntax hints:   → wi 4   = wceq 1543  WLimcwlim 33485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-8 2114  ax-9 2122  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2073  df-clab 2715  df-cleq 2728  df-clel 2809  df-ne 2933  df-ral 3056  df-rex 3057  df-rab 3060  df-v 3400  df-dif 3856  df-un 3858  df-in 3860  df-ss 3870  df-nul 4224  df-if 4426  df-sn 4528  df-pr 4530  df-op 4534  df-uni 4806  df-br 5040  df-opab 5102  df-xp 5542  df-cnv 5544  df-dm 5546  df-rn 5547  df-res 5548  df-ima 5549  df-pred 6140  df-sup 9036  df-inf 9037  df-wlim 33487

This theorem is referenced by: (None)