Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > funfvima2 | Unicode version |
Description: A function's value in an included preimage belongs to the image. (Contributed by NM, 3-Feb-1997.) |
Ref | Expression |
---|---|
funfvima2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3122 | . . 3 | |
2 | funfvima 5700 | . . . . . 6 | |
3 | 2 | ex 114 | . . . . 5 |
4 | 3 | com23 78 | . . . 4 |
5 | 4 | a2d 26 | . . 3 |
6 | 1, 5 | syl5 32 | . 2 |
7 | 6 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2128 wss 3102 cdm 4588 cima 4591 wfun 5166 cfv 5172 |
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 4084 ax-pow 4137 ax-pr 4171 |
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 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-ima 4601 df-iota 5137 df-fun 5174 df-fn 5175 df-fv 5180 |
This theorem is referenced by: fnfvima 5703 phimullem 12115 qtopbasss 12991 tgqioo 13017 |
Copyright terms: Public domain | W3C validator |