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Mirrors > Home > MPE Home > Th. List > fvixp | Structured version Visualization version 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 7912 | . . 3 | |
2 | 1 | simp3bi 1078 | . 2 |
3 | fveq2 6191 | . . . 4 | |
4 | fvixp.1 | . . . 4 | |
5 | 3, 4 | eleq12d 2695 | . . 3 |
6 | 5 | rspccva 3308 | . 2 |
7 | 2, 6 | sylan 488 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 cvv 3200 wfn 5883 cfv 5888 cixp 7908 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 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-uni 4437 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-ixp 7909 |
This theorem is referenced by: funcf2 16528 funcpropd 16560 natcl 16613 natpropd 16636 finixpnum 33394 hspdifhsp 40830 |
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