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Mirrors > Home > NFE Home > Th. List > reu7 | Unicode version |
Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
rmo4.1 |
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Ref | Expression |
---|---|
reu7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reu3 3027 |
. 2
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2 | rmo4.1 |
. . . . . . 7
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3 | eqeq1 2359 |
. . . . . . . 8
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4 | eqcom 2355 |
. . . . . . . 8
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5 | 3, 4 | syl6bb 252 |
. . . . . . 7
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6 | 2, 5 | imbi12d 311 |
. . . . . 6
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7 | 6 | cbvralv 2836 |
. . . . 5
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8 | 7 | rexbii 2640 |
. . . 4
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9 | eqeq1 2359 |
. . . . . . 7
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10 | 9 | imbi2d 307 |
. . . . . 6
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11 | 10 | ralbidv 2635 |
. . . . 5
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12 | 11 | cbvrexv 2837 |
. . . 4
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13 | 8, 12 | bitri 240 |
. . 3
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14 | 13 | anbi2i 675 |
. 2
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15 | 1, 14 | bitri 240 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ral 2620 df-rex 2621 df-reu 2622 df-rmo 2623 |
This theorem is referenced by: (None) |
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