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Mirrors > Home > ILE Home > Th. List > ax11v | Unicode version |
Description: This is a version of ax-11o 1796 when the variables are distinct. Axiom (C8) of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.) (Revised by Jim Kingdon, 15-Dec-2017.) |
Ref | Expression |
---|---|
ax11v |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1675 |
. 2
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2 | ax-17 1507 |
. . . . 5
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3 | ax-11 1485 |
. . . . 5
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4 | 2, 3 | syl5 32 |
. . . 4
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5 | equequ2 1690 |
. . . . 5
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6 | 5 | imbi1d 230 |
. . . . . . 7
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7 | 6 | albidv 1797 |
. . . . . 6
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8 | 7 | imbi2d 229 |
. . . . 5
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9 | 5, 8 | imbi12d 233 |
. . . 4
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10 | 4, 9 | mpbii 147 |
. . 3
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11 | 10 | exlimiv 1578 |
. 2
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12 | 1, 11 | ax-mp 5 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-17 1507 ax-i9 1511 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: equs5or 1803 sb56 1858 |
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