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Mirrors > Home > MPE Home > Th. List > rexxp | Structured version Visualization version Unicode version |
Description: Existential quantification restricted to a Cartesian product is equivalent to a double restricted quantification. (Contributed by NM, 11-Nov-1995.) (Revised by Mario Carneiro, 14-Feb-2015.) |
Ref | Expression |
---|---|
ralxp.1 |
Ref | Expression |
---|---|
rexxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunxpconst 5175 | . . 3 | |
2 | 1 | rexeqi 3143 | . 2 |
3 | ralxp.1 | . . 3 | |
4 | 3 | rexiunxp 5262 | . 2 |
5 | 2, 4 | bitr3i 266 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wrex 2913 csn 4177 cop 4183 ciun 4520 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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-sbc 3436 df-csb 3534 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-iun 4522 df-opab 4713 df-xp 5120 df-rel 5121 |
This theorem is referenced by: exopxfr 5265 fnrnov 6807 foov 6808 ovelimab 6812 el2xptp 7211 xpf1o 8122 xpwdomg 8490 hsmexlem2 9249 cnref1o 11827 vdwmc 15682 arwhoma 16695 txbas 21370 txkgen 21455 xrofsup 29533 elunirnmbfm 30315 madeval2 31936 rmxypairf1o 37476 unxpwdom3 37665 |
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