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Mirrors > Home > MPE Home > Th. List > rexcom13 | Structured version Unicode version |
Description: Swap 1st and 3rd restricted existential quantifiers. (Contributed by NM, 8-Apr-2015.) |
Ref | Expression |
---|---|
rexcom13 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom 2988 |
. 2
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2 | rexcom 2988 |
. . 3
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3 | 2 | rexbii 2862 |
. 2
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4 | rexcom 2988 |
. 2
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5 | 1, 3, 4 | 3bitri 271 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-cleq 2446 df-clel 2449 df-nfc 2604 df-rex 2805 |
This theorem is referenced by: rexrot4 2990 |
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