![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > cnvimass | GIF version |
Description: A preimage under any class is included in the domain of the class. (Contributed by FL, 29-Jan-2007.) |
Ref | Expression |
---|---|
cnvimass | ⊢ (◡𝐴 “ 𝐵) ⊆ dom 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imassrn 4981 | . 2 ⊢ (◡𝐴 “ 𝐵) ⊆ ran ◡𝐴 | |
2 | dfdm4 4819 | . 2 ⊢ dom 𝐴 = ran ◡𝐴 | |
3 | 1, 2 | sseqtrri 3190 | 1 ⊢ (◡𝐴 “ 𝐵) ⊆ dom 𝐴 |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3129 ◡ccnv 4625 dom cdm 4626 ran crn 4627 “ cima 4629 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-br 4004 df-opab 4065 df-xp 4632 df-cnv 4634 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 |
This theorem is referenced by: fvimacnvi 5630 elpreima 5635 fconst4m 5736 nn0supp 9227 fisumss 11399 fprodssdc 11597 1arith 12364 cnpnei 13655 cnclima 13659 cnntri 13660 cnntr 13661 cncnp 13666 cnrest2 13672 cndis 13677 txcnmpt 13709 txdis1cn 13714 hmeoimaf1o 13750 xmeter 13872 |
Copyright terms: Public domain | W3C validator |