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Mirrors > Home > ILE Home > Th. List > funmpt2 | Unicode version |
Description: Functionality of a class given by a maps-to notation. (Contributed by FL, 17-Feb-2008.) (Revised by Mario Carneiro, 31-May-2014.) |
Ref | Expression |
---|---|
funmpt2.1 |
Ref | Expression |
---|---|
funmpt2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funmpt 5131 | . 2 | |
2 | funmpt2.1 | . . 3 | |
3 | 2 | funeqi 5114 | . 2 |
4 | 1, 3 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 cmpt 3959 wfun 5087 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-fun 5095 |
This theorem is referenced by: fvmptss2 5464 mptrcl 5471 elfvmptrab1 5483 frectfr 6265 frecsuclem 6271 caseinj 6942 caseinl 6944 caseinr 6945 omp1eomlem 6947 djudoml 7043 djudomr 7044 fihashf1rn 10503 funtopon 12106 eltg4i 12151 eltg3 12153 tg1 12155 tg2 12156 tgclb 12161 lmrcl 12287 exmidsbthrlem 13144 |
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