Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fmptap | Unicode version |
Description: Append an additional value to a function. (Contributed by NM, 6-Jun-2006.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
fmptap.0a | |
fmptap.0b | |
fmptap.1 | |
fmptap.2 |
Ref | Expression |
---|---|
fmptap |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmptap.0a | . . . . 5 | |
2 | fmptap.0b | . . . . 5 | |
3 | fmptsn 5373 | . . . . 5 | |
4 | 1, 2, 3 | mp2an 416 | . . . 4 |
5 | elsni 3416 | . . . . . 6 | |
6 | fmptap.2 | . . . . . 6 | |
7 | 5, 6 | syl 14 | . . . . 5 |
8 | 7 | mpteq2ia 3864 | . . . 4 |
9 | 4, 8 | eqtr4i 2104 | . . 3 |
10 | 9 | uneq2i 3123 | . 2 |
11 | mptun 5049 | . 2 | |
12 | fmptap.1 | . . 3 | |
13 | mpteq1 3862 | . . 3 | |
14 | 12, 13 | ax-mp 7 | . 2 |
15 | 10, 11, 14 | 3eqtr2i 2107 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 cvv 2601 cun 2971 csn 3398 cop 3401 cmpt 3839 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-reu 2355 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |