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Theorem leeq1d 39870
 Description: Specialization of breq1d 4940 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 4954 1 (𝜑𝐵𝐶)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1507   ∈ wcel 2050   class class class wbr 4930  ℝcr 10336   ≤ cle 10477 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2750 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-rab 3097  df-v 3417  df-dif 3834  df-un 3836  df-in 3838  df-ss 3845  df-nul 4181  df-if 4352  df-sn 4443  df-pr 4445  df-op 4449  df-br 4931 This theorem is referenced by:  imo72b2lem0  39880
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