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Mirrors > Home > ILE Home > Th. List > foelrn | Unicode version |
Description: Property of a surjective function. (Contributed by Jeff Madsen, 4-Jan-2011.) (Proof shortened by BJ, 6-Jul-2022.) |
Ref | Expression |
---|---|
foelrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | foima2 5703 | . 2 | |
2 | 1 | biimpa 294 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 wrex 2436 wfo 5169 cfv 5171 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-br 3967 df-opab 4027 df-id 4254 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-rn 4598 df-res 4599 df-ima 4600 df-iota 5136 df-fun 5173 df-fn 5174 df-f 5175 df-fo 5177 df-fv 5179 |
This theorem is referenced by: foco2 5705 ctmlemr 7053 ctm 7054 ctssdclemn0 7055 ctssdccl 7056 ctssdc 7058 enumctlemm 7059 fodju0 7091 exmidfodomrlemr 7138 exmidfodomrlemrALT 7139 ennnfonelemrn 12190 ctinf 12201 ctiunctlemfo 12210 subctctexmid 13615 pw1nct 13617 |
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