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Mirrors > Home > MPE Home > Th. List > 2eu7 | Structured version Unicode version |
Description: Two equivalent expressions for double existential uniqueness. (Contributed by NM, 19-Feb-2005.) |
Ref | Expression |
---|---|
2eu7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 1780 |
. . . 4
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2 | 1 | nfeu 2281 |
. . 3
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3 | 2 | euan 2340 |
. 2
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4 | ancom 450 |
. . . . 5
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5 | 4 | eubii 2287 |
. . . 4
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6 | nfe1 1780 |
. . . . 5
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7 | 6 | euan 2340 |
. . . 4
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8 | ancom 450 |
. . . 4
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9 | 5, 7, 8 | 3bitri 271 |
. . 3
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10 | 9 | eubii 2287 |
. 2
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11 | ancom 450 |
. 2
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12 | 3, 10, 11 | 3bitr4ri 278 |
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 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-eu 2266 |
This theorem is referenced by: 2eu8 2383 |
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