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Theorem mpteq1i 4772
Description: An equality theorem for the maps to notation. (Contributed by Glauco Siliprandi, 17-Aug-2020.)
Hypothesis
Ref Expression
mpteq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
mpteq1i (𝑥𝐴𝐶) = (𝑥𝐵𝐶)
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵
Allowed substitution hint:   𝐶(𝑥)

Proof of Theorem mpteq1i
StepHypRef Expression
1 mpteq1i.1 . 2 𝐴 = 𝐵
2 mpteq1 4770 . 2 (𝐴 = 𝐵 → (𝑥𝐴𝐶) = (𝑥𝐵𝐶))
31, 2ax-mp 5 1 (𝑥𝐴𝐶) = (𝑥𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  cmpt 4762
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-ral 2946  df-opab 4746  df-mpt 4763
This theorem is referenced by:  wlknwwlksnbij2  26846  wlkwwlkbij2  26853  wwlksnextbij  26865  limsupequzmptlem  40278  sge0iunmptlemfi  40948  sge0iunmpt  40953  hoidmvlelem3  41132  smfmulc1  41324  smflimsuplem2  41348
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