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Theorem leeq1d 42371
Description: Specialization of breq1d 5113 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 5127 1 (𝜑𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1541  wcel 2106   class class class wbr 5103  cr 11046  cle 11186
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3406  df-v 3445  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4281  df-if 4485  df-sn 4585  df-pr 4587  df-op 4591  df-br 5104
This theorem is referenced by:  imo72b2lem0  42380
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