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Mirrors > Home > ILE Home > Th. List > elmpocl1 | Unicode version |
Description: If a two-parameter class is inhabited, the first argument is in its nominal domain. (Contributed by FL, 15-Oct-2012.) (Revised by Stefan O'Rear, 7-Mar-2015.) |
Ref | Expression |
---|---|
elmpocl.f |
Ref | Expression |
---|---|
elmpocl1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elmpocl.f | . . 3 | |
2 | 1 | elmpocl 6031 | . 2 |
3 | 2 | simpld 111 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 (class class class)co 5837 cmpo 5839 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-opab 4039 df-id 4266 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-iota 5148 df-fun 5185 df-fv 5191 df-ov 5840 df-oprab 5841 df-mpo 5842 |
This theorem is referenced by: pmresg 6634 iccssico2 9875 elfzoel1 10071 cncfrss 13129 limccl 13195 |
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