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Mirrors > Home > NFE Home > Th. List > aev-o | Unicode version |
Description: A "distinctor elimination" lemma with no restrictions on variables in the consequent, proved without using ax-16 2144. Version of aev 1991 using ax-10o 2139. (Contributed by NM, 8-Nov-2006.) (Proof shortened by Andrew Salmon, 21-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
aev-o |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbae-o 2153 |
. 2
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2 | hbae-o 2153 |
. . . 4
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3 | ax-8 1675 |
. . . . 5
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4 | 3 | spimv 1990 |
. . . 4
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5 | 2, 4 | alrimih 1565 |
. . 3
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6 | ax-8 1675 |
. . . . . . . 8
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7 | equcomi 1679 |
. . . . . . . 8
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8 | 6, 7 | syl6 29 |
. . . . . . 7
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9 | 8 | spimv 1990 |
. . . . . 6
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10 | 9 | aecoms-o 2152 |
. . . . 5
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11 | 10 | a5i-o 2150 |
. . . 4
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12 | hbae-o 2153 |
. . . . 5
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13 | ax-8 1675 |
. . . . . 6
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14 | 13 | spimv 1990 |
. . . . 5
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15 | 12, 14 | alrimih 1565 |
. . . 4
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16 | aecom-o 2151 |
. . . 4
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17 | 11, 15, 16 | 3syl 18 |
. . 3
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18 | ax-8 1675 |
. . . 4
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19 | 18 | spimv 1990 |
. . 3
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20 | 5, 17, 19 | 3syl 18 |
. 2
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21 | 1, 20 | alrimih 1565 |
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-4 2135 ax-5o 2136 ax-6o 2137 ax-10o 2139 ax-12o 2142 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: a16g-o 2186 |
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