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Mirrors > Home > ILE Home > Th. List > fmptapd | Unicode version |
Description: Append an additional value to a function. (Contributed by Thierry Arnoux, 3-Jan-2017.) |
Ref | Expression |
---|---|
fmptapd.0a | |
fmptapd.0b | |
fmptapd.1 | |
fmptapd.2 |
Ref | Expression |
---|---|
fmptapd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmptapd.0a | . . . . 5 | |
2 | fmptapd.0b | . . . . 5 | |
3 | fmptsn 5602 | . . . . 5 | |
4 | 1, 2, 3 | syl2anc 408 | . . . 4 |
5 | elsni 3540 | . . . . . 6 | |
6 | fmptapd.2 | . . . . . 6 | |
7 | 5, 6 | sylan2 284 | . . . . 5 |
8 | 7 | mpteq2dva 4013 | . . . 4 |
9 | 4, 8 | eqtr4d 2173 | . . 3 |
10 | 9 | uneq2d 3225 | . 2 |
11 | mptun 5249 | . . 3 | |
12 | 11 | a1i 9 | . 2 |
13 | fmptapd.1 | . . 3 | |
14 | 13 | mpteq1d 4008 | . 2 |
15 | 10, 12, 14 | 3eqtr2d 2176 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cvv 2681 cun 3064 csn 3522 cop 3525 cmpt 3984 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-reu 2421 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 df-fo 5124 df-f1o 5125 |
This theorem is referenced by: fmptpr 5605 |
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