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Mirrors > Home > MPE Home > Th. List > ltrelre | Structured version Visualization version Unicode version |
Description: 'Less than' is a relation on real numbers. (Contributed by NM, 22-Feb-1996.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ltrelre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lt 9949 | . 2 | |
2 | opabssxp 5193 | . 2 | |
3 | 1, 2 | eqsstri 3635 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wex 1704 wcel 1990 wss 3574 cop 4183 class class class wbr 4653 copab 4712 cxp 5112 c0r 9688 cltr 9693 cr 9935 cltrr 9940 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-in 3581 df-ss 3588 df-opab 4713 df-xp 5120 df-lt 9949 |
This theorem is referenced by: ltresr 9961 |
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