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Mirrors > Home > ILE Home > Th. List > mptrabex | Unicode version |
Description: If the domain of a function given by maps-to notation is a class abstraction based on a set, the function is a set. (Contributed by AV, 16-Jul-2019.) (Revised by AV, 26-Mar-2021.) |
Ref | Expression |
---|---|
mptrabex.1 |
Ref | Expression |
---|---|
mptrabex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mptrabex.1 | . . 3 | |
2 | 1 | rabex 4134 | . 2 |
3 | 2 | mptex 5726 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2142 crab 2453 cvv 2731 cmpt 4051 |
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 705 ax-5 1441 ax-7 1442 ax-gen 1443 ax-ie1 1487 ax-ie2 1488 ax-8 1498 ax-10 1499 ax-11 1500 ax-i12 1501 ax-bndl 1503 ax-4 1504 ax-17 1520 ax-i9 1524 ax-ial 1528 ax-i5r 1529 ax-14 2145 ax-ext 2153 ax-coll 4105 ax-sep 4108 ax-pow 4161 ax-pr 4195 |
This theorem depends on definitions: df-bi 116 df-3an 976 df-tru 1352 df-nf 1455 df-sb 1757 df-eu 2023 df-mo 2024 df-clab 2158 df-cleq 2164 df-clel 2167 df-nfc 2302 df-ral 2454 df-rex 2455 df-reu 2456 df-rab 2458 df-v 2733 df-sbc 2957 df-csb 3051 df-un 3126 df-in 3128 df-ss 3135 df-pw 3569 df-sn 3590 df-pr 3591 df-op 3593 df-uni 3798 df-iun 3876 df-br 3991 df-opab 4052 df-mpt 4053 df-id 4279 df-xp 4618 df-rel 4619 df-cnv 4620 df-co 4621 df-dm 4622 df-rn 4623 df-res 4624 df-ima 4625 df-iota 5162 df-fun 5202 df-fn 5203 df-f 5204 df-f1 5205 df-fo 5206 df-f1o 5207 df-fv 5208 |
This theorem is referenced by: odzval 12199 |
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