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Theorem leeq2d 40794
 Description: Specialization of breq2d 5054 to reals and less than. (Contributed by Stanislas Polu, 9-Mar-2020.)
Hypotheses
Ref Expression
leeq2d.1 (𝜑𝐴𝐶)
leeq2d.2 (𝜑𝐶 = 𝐷)
leeq2d.3 (𝜑𝐴 ∈ ℝ)
leeq2d.4 (𝜑𝐶 ∈ ℝ)
Assertion
Ref Expression
leeq2d (𝜑𝐴𝐷)

Proof of Theorem leeq2d
StepHypRef Expression
1 leeq2d.1 . 2 (𝜑𝐴𝐶)
2 leeq2d.2 . 2 (𝜑𝐶 = 𝐷)
31, 2breqtrd 5068 1 (𝜑𝐴𝐷)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   ∈ wcel 2114   class class class wbr 5042  ℝcr 10525   ≤ cle 10665 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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-un 3913  df-sn 4540  df-pr 4542  df-op 4546  df-br 5043 This theorem is referenced by:  imo72b2lem0  40802
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