Theorem wlimeq2 35422

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 2727	. 2 ⊢ 𝑅 = 𝑅
2		wlimeq12 35420	. 2 ⊢ ((𝑅 = 𝑅 ∧ 𝐴 = 𝐵) → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))
3	1, 2	mpan 688	1 ⊢ (𝐴 = 𝐵 → WLim(𝑅, 𝐴) = WLim(𝑅, 𝐵))

Syntax hints:   → wi 4   = wceq 1533  WLimcwlim 35412

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 2698

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-ne 2937  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4911  df-br 5151  df-opab 5213  df-xp 5686  df-cnv 5688  df-dm 5690  df-rn 5691  df-res 5692  df-ima 5693  df-pred 6308  df-sup 9471  df-inf 9472  df-wlim 35414

This theorem is referenced by: (None)