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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 2799 | . 2 ⊢ ∅ = ∅ | |
2 | f1o00 6390 | . 2 ⊢ (∅:∅–1-1-onto→∅ ↔ (∅ = ∅ ∧ ∅ = ∅)) | |
3 | 1, 1, 2 | mpbir2an 703 | 1 ⊢ ∅:∅–1-1-onto→∅ |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1653 ∅c0 4115 –1-1-onto→wf1o 6100 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 ax-5 2006 ax-6 2072 ax-7 2107 ax-9 2166 ax-10 2185 ax-11 2200 ax-12 2213 ax-13 2377 ax-ext 2777 ax-sep 4975 ax-nul 4983 ax-pr 5097 |
This theorem depends on definitions: df-bi 199 df-an 386 df-or 875 df-3an 1110 df-tru 1657 df-ex 1876 df-nf 1880 df-sb 2065 df-mo 2591 df-eu 2609 df-clab 2786 df-cleq 2792 df-clel 2795 df-nfc 2930 df-ral 3094 df-rex 3095 df-rab 3098 df-v 3387 df-dif 3772 df-un 3774 df-in 3776 df-ss 3783 df-nul 4116 df-if 4278 df-sn 4369 df-pr 4371 df-op 4375 df-br 4844 df-opab 4906 df-id 5220 df-xp 5318 df-rel 5319 df-cnv 5320 df-co 5321 df-dm 5322 df-rn 5323 df-fun 6103 df-fn 6104 df-f 6105 df-f1 6106 df-fo 6107 df-f1o 6108 |
This theorem is referenced by: brwdom2 8720 cnfcom 8847 ackbij2lem2 9350 eupth0 27558 f1ocnt 30077 iso0 39284 |
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