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Mirrors > Home > MPE Home > Th. List > sbcimdv | Structured version Unicode version |
Description: Substitution analog of Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 11-Nov-2005.) |
Ref | Expression |
---|---|
sbcimdv.1 |
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Ref | Expression |
---|---|
sbcimdv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcimdv.1 |
. . . 4
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2 | 1 | alrimiv 1686 |
. . 3
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3 | spsbc 3283 |
. . 3
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4 | sbcim1 3319 |
. . 3
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5 | 2, 3, 4 | syl56 34 |
. 2
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6 | sbcex 3280 |
. . . . 5
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7 | 6 | con3i 135 |
. . . 4
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8 | 7 | pm2.21d 106 |
. . 3
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9 | 8 | a1d 25 |
. 2
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10 | 5, 9 | pm2.61i 164 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1709 ax-7 1729 ax-10 1776 ax-12 1793 ax-13 1944 ax-ext 2429 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1702 df-clab 2436 df-cleq 2442 df-clel 2445 df-v 3056 df-sbc 3271 |
This theorem is referenced by: (None) |
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