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Theorem leeq1d 40385
Description: Specialization of breq1d 5067 to reals and less than. (Contributed by Stanislas Polu, 9-Mar-2020.)
Hypotheses
Ref Expression
leeq1d.1 (𝜑𝐴𝐶)
leeq1d.2 (𝜑𝐴 = 𝐵)
leeq1d.3 (𝜑𝐴 ∈ ℝ)
leeq1d.4 (𝜑𝐶 ∈ ℝ)
Assertion
Ref Expression
leeq1d (𝜑𝐵𝐶)

Proof of Theorem leeq1d
StepHypRef Expression
1 leeq1d.2 . 2 (𝜑𝐴 = 𝐵)
2 leeq1d.1 . 2 (𝜑𝐴𝐶)
31, 2eqbrtrrd 5081 1 (𝜑𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1528  wcel 2105   class class class wbr 5057  cr 10524  cle 10664
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564  df-br 5058
This theorem is referenced by:  imo72b2lem0  40394
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