![]() |
Mathbox for Stanislas Polu |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > leeq2d | Structured version Visualization version GIF version |
Description: Specialization of breq2d 5042 to reals and less than. (Contributed by Stanislas Polu, 9-Mar-2020.) |
Ref | Expression |
---|---|
leeq2d.1 | ⊢ (𝜑 → 𝐴 ≤ 𝐶) |
leeq2d.2 | ⊢ (𝜑 → 𝐶 = 𝐷) |
leeq2d.3 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
leeq2d.4 | ⊢ (𝜑 → 𝐶 ∈ ℝ) |
Ref | Expression |
---|---|
leeq2d | ⊢ (𝜑 → 𝐴 ≤ 𝐷) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leeq2d.1 | . 2 ⊢ (𝜑 → 𝐴 ≤ 𝐶) | |
2 | leeq2d.2 | . 2 ⊢ (𝜑 → 𝐶 = 𝐷) | |
3 | 1, 2 | breqtrd 5056 | 1 ⊢ (𝜑 → 𝐴 ≤ 𝐷) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1538 ∈ wcel 2111 class class class wbr 5030 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 2113 ax-9 2121 ax-ext 2770 |
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 2777 df-cleq 2791 df-clel 2870 df-v 3443 df-un 3886 df-sn 4526 df-pr 4528 df-op 4532 df-br 5031 |
This theorem is referenced by: imo72b2lem0 40869 |
Copyright terms: Public domain | W3C validator |