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Mirrors > Home > MPE Home > Th. List > nfxp | Structured version Visualization version Unicode version |
Description: Bound-variable hypothesis builder for Cartesian product. (Contributed by NM, 15-Sep-2003.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfxp.1 | |
nfxp.2 |
Ref | Expression |
---|---|
nfxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xp 5120 | . 2 | |
2 | nfxp.1 | . . . . 5 | |
3 | 2 | nfcri 2758 | . . . 4 |
4 | nfxp.2 | . . . . 5 | |
5 | 4 | nfcri 2758 | . . . 4 |
6 | 3, 5 | nfan 1828 | . . 3 |
7 | 6 | nfopab 4718 | . 2 |
8 | 1, 7 | nfcxfr 2762 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wcel 1990 wnfc 2751 copab 4712 cxp 5112 |
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-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-opab 4713 df-xp 5120 |
This theorem is referenced by: opeliunxp 5170 nfres 5398 mpt2mptsx 7233 dmmpt2ssx 7235 fmpt2x 7236 ovmptss 7258 axcc2 9259 fsum2dlem 14501 fsumcom2 14505 fsumcom2OLD 14506 fprod2dlem 14710 fprodcom2 14714 fprodcom2OLD 14715 gsumcom2 18374 prdsdsf 22172 prdsxmet 22174 aciunf1lem 29462 esum2dlem 30154 poimirlem16 33425 poimirlem19 33428 dvnprodlem1 40161 stoweidlem21 40238 stoweidlem47 40264 opeliun2xp 42111 dmmpt2ssx2 42115 |
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