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Mirrors > Home > MPE Home > Th. List > f1o0 | Structured version Visualization version GIF version |
Description: One-to-one onto mapping of the empty set. (Contributed by NM, 10-Sep-2004.) |
Ref | Expression |
---|---|
f1o0 | ⊢ ∅:∅–1-1-onto→∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2726 | . 2 ⊢ ∅ = ∅ | |
2 | f1o00 6868 | . 2 ⊢ (∅:∅–1-1-onto→∅ ↔ (∅ = ∅ ∧ ∅ = ∅)) | |
3 | 1, 1, 2 | mpbir2an 709 | 1 ⊢ ∅:∅–1-1-onto→∅ |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 ∅c0 4323 –1-1-onto→wf1o 6543 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-12 2167 ax-ext 2697 ax-sep 5295 ax-nul 5302 ax-pr 5424 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-mo 2529 df-clab 2704 df-cleq 2718 df-clel 2803 df-ral 3052 df-rex 3061 df-rab 3421 df-v 3465 df-dif 3950 df-un 3952 df-ss 3964 df-nul 4324 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-br 5145 df-opab 5207 df-id 5571 df-xp 5679 df-rel 5680 df-cnv 5681 df-co 5682 df-dm 5683 df-rn 5684 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 |
This theorem is referenced by: en0 9039 en0OLD 9040 en0r 9042 brwdom2 9607 cnfcom 9734 ackbij2lem2 10272 eupth0 30142 f1ocnt 32705 1arithidom 33416 iso0 44016 |
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