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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 |
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funmpt2.1 |
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Ref | Expression |
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funmpt2 |
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Step | Hyp | Ref | Expression |
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1 | funmpt 5266 |
. 2
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2 | funmpt2.1 |
. . 3
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3 | 2 | funeqi 5249 |
. 2
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4 | 1, 3 | mpbir 146 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-opab 4077 df-mpt 4078 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-fun 5230 |
This theorem is referenced by: fvmptss2 5604 mptrcl 5611 elfvmptrab1 5623 frectfr 6415 frecsuclem 6421 caseinj 7102 caseinl 7104 caseinr 7105 omp1eomlem 7107 djudoml 7232 djudomr 7233 fihashf1rn 10782 lidlmex 13664 funtopon 13808 eltg4i 13851 eltg3 13853 tg1 13855 tg2 13856 tgclb 13861 lmrcl 13987 exmidsbthrlem 15067 |
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