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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax6e2eq | Structured version Visualization version Unicode version |
Description: Alternate form of ax6e 2093
for non-distinct ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ax6e2eq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6ev 1806 |
. . . . . . 7
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2 | hbae 2148 |
. . . . . . . 8
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3 | ax7 1859 |
. . . . . . . . . 10
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4 | 3 | sps 1942 |
. . . . . . . . 9
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5 | 4 | ancld 556 |
. . . . . . . 8
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6 | 2, 5 | eximdh 1723 |
. . . . . . 7
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7 | 1, 6 | mpi 20 |
. . . . . 6
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8 | 7 | axc4i 1979 |
. . . . 5
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9 | axc11 2147 |
. . . . 5
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10 | 8, 9 | mpd 15 |
. . . 4
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11 | 19.2 1808 |
. . . 4
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12 | 10, 11 | syl 17 |
. . 3
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13 | excomim 1928 |
. . 3
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14 | 12, 13 | syl 17 |
. 2
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15 | equtrr 1865 |
. . . 4
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16 | 15 | anim2d 568 |
. . 3
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17 | 16 | 2eximdv 1765 |
. 2
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18 | 14, 17 | syl5com 31 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1663 df-nf 1667 |
This theorem is referenced by: ax6e2ndeq 36920 ax6e2ndeqVD 37300 ax6e2ndeqALT 37322 |
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