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Mirrors > Home > ILE Home > Th. List > fvixp | Unicode version |
Description: Projection of a factor of an indexed Cartesian product. (Contributed by Mario Carneiro, 11-Jun-2016.) |
Ref | Expression |
---|---|
fvixp.1 |
Ref | Expression |
---|---|
fvixp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elixp2 6659 | . . 3 | |
2 | 1 | simp3bi 1003 | . 2 |
3 | fveq2 5480 | . . . 4 | |
4 | fvixp.1 | . . . 4 | |
5 | 3, 4 | eleq12d 2235 | . . 3 |
6 | 5 | rspccva 2824 | . 2 |
7 | 2, 6 | sylan 281 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 wral 2442 cvv 2721 wfn 5177 cfv 5182 cixp 6655 |
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-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fn 5185 df-fv 5190 df-ixp 6656 |
This theorem is referenced by: (None) |
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