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Theorem leeq2d 37476
 Description: Specialization of breq2d 4595 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 . . 3 (𝜑𝐶 = 𝐷)
32breq2d 4595 . 2 (𝜑 → (𝐴𝐶𝐴𝐷))
41, 3mpbid 221 1 (𝜑𝐴𝐷)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ∈ wcel 1977   class class class wbr 4583  ℝcr 9814   ≤ cle 9954 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584 This theorem is referenced by:  imo72b2lem0  37487
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