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Mirrors > Home > MPE Home > Th. List > equveli | Structured version Visualization version Unicode version |
Description: A variable elimination law for equality with no distinct variable requirements. Compare equvini 2179. (Contributed by NM, 1-Mar-2013.) (Proof shortened by Mario Carneiro, 17-Oct-2016.) (Proof shortened by Wolf Lammen, 15-Jun-2019.) |
Ref | Expression |
---|---|
equveli |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | albi 1690 |
. 2
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2 | ax6e 2094 |
. . . 4
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3 | biimpr 202 |
. . . . . 6
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4 | ax7 1860 |
. . . . . 6
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5 | 3, 4 | syli 38 |
. . . . 5
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6 | 5 | com12 32 |
. . . 4
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7 | 2, 6 | eximii 1709 |
. . 3
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8 | 7 | 19.35i 1741 |
. 2
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9 | 4 | spsd 1945 |
. . . . 5
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10 | 9 | sps 1943 |
. . . 4
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11 | 10 | a1dd 47 |
. . 3
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12 | nfeqf 2139 |
. . . . 5
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13 | 12 | 19.9d 1968 |
. . . 4
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14 | 13 | ex 436 |
. . 3
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15 | 11, 14 | bija 357 |
. 2
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16 | 1, 8, 15 | sylc 62 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1664 df-nf 1668 |
This theorem is referenced by: (None) |
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