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Mirrors > Home > MPE Home > Th. List > fmptapd | Structured version Visualization version 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.2 | . . . 4 | |
2 | fmptapd.0a | . . . 4 | |
3 | fmptapd.0b | . . . 4 | |
4 | 1, 2, 3 | fmptsnd 6435 | . . 3 |
5 | 4 | uneq2d 3767 | . 2 |
6 | mptun 6025 | . . 3 | |
7 | 6 | a1i 11 | . 2 |
8 | fmptapd.1 | . . 3 | |
9 | 8 | mpteq1d 4738 | . 2 |
10 | 5, 7, 9 | 3eqtr2d 2662 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 cun 3572 csn 4177 cop 4183 cmpt 4729 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-opab 4713 df-mpt 4730 |
This theorem is referenced by: fmptpr 6438 poimirlem3 33412 poimirlem4 33413 poimirlem16 33425 poimirlem17 33426 poimirlem19 33428 poimirlem20 33429 |
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