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Mirrors > Home > NFE Home > Th. List > ax11indi | Unicode version |
Description: Induction step for constructing a substitution instance of ax-11o 2141 without using ax-11o 2141. Implication case. (Contributed by NM, 21-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax11indn.1 |
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ax11indi.2 |
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Ref | Expression |
---|---|
ax11indi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax11indn.1 |
. . . . . 6
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2 | 1 | ax11indn 2195 |
. . . . 5
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3 | 2 | imp 418 |
. . . 4
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4 | pm2.21 100 |
. . . . . 6
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5 | 4 | imim2i 13 |
. . . . 5
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6 | 5 | alimi 1559 |
. . . 4
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7 | 3, 6 | syl6 29 |
. . 3
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8 | ax11indi.2 |
. . . . 5
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9 | 8 | imp 418 |
. . . 4
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10 | ax-1 6 |
. . . . . 6
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11 | 10 | imim2i 13 |
. . . . 5
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12 | 11 | alimi 1559 |
. . . 4
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13 | 9, 12 | syl6 29 |
. . 3
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14 | 7, 13 | jad 154 |
. 2
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15 | 14 | ex 423 |
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-11 1746 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 |
This theorem is referenced by: (None) |
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