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Mirrors > Home > MPE Home > Th. List > rel0 | Structured version Visualization version Unicode version |
Description: The empty set is a relation. (Contributed by NM, 26-Apr-1998.) |
Ref | Expression |
---|---|
rel0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ss 3972 | . 2 | |
2 | df-rel 5121 | . 2 | |
3 | 1, 2 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cvv 3200 wss 3574 c0 3915 cxp 5112 wrel 5119 |
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-v 3202 df-dif 3577 df-in 3581 df-ss 3588 df-nul 3916 df-rel 5121 |
This theorem is referenced by: reldm0 5343 cnv0OLD 5536 cnveq0 5591 co02 5649 co01 5650 tpos0 7382 0we1 7586 0er 7780 0erOLD 7781 canthwe 9473 opabf 34131 dibvalrel 36452 dicvalrelN 36474 dihvalrel 36568 |
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