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Mirrors > Home > MPE Home > Th. List > r2exf | Structured version Unicode version |
Description: Double restricted existential quantification. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
r2alf.1 |
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Ref | Expression |
---|---|
r2exf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2805 |
. 2
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2 | r2alf.1 |
. . . . . 6
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3 | 2 | nfcri 2609 |
. . . . 5
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4 | 3 | 19.42 1912 |
. . . 4
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5 | anass 649 |
. . . . 5
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6 | 5 | exbii 1635 |
. . . 4
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7 | df-rex 2805 |
. . . . 5
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8 | 7 | anbi2i 694 |
. . . 4
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9 | 4, 6, 8 | 3bitr4i 277 |
. . 3
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10 | 9 | exbii 1635 |
. 2
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11 | 1, 10 | bitr4i 252 |
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-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: r2ex 2878 rexcomf 2986 |
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