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Theorem leeq2d 42411
Description: Specialization of breq2d 5117 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 5131 1 (𝜑𝐴𝐷)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1541  wcel 2106   class class class wbr 5105  cr 11049  cle 11189
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 3408  df-v 3447  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4283  df-if 4487  df-sn 4587  df-pr 4589  df-op 4593  df-br 5106
This theorem is referenced by:  imo72b2lem0  42419
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