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Mirrors > Home > MPE Home > Th. List > rspc2 | Structured version Visualization version Unicode version |
Description: 2-variable restricted specialization, using implicit substitution. (Contributed by NM, 9-Nov-2012.) |
Ref | Expression |
---|---|
rspc2.1 |
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rspc2.2 |
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rspc2.3 |
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rspc2.4 |
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Ref | Expression |
---|---|
rspc2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2592 |
. . . 4
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2 | rspc2.1 |
. . . 4
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3 | 1, 2 | nfral 2769 |
. . 3
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4 | rspc2.3 |
. . . 4
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5 | 4 | ralbidv 2809 |
. . 3
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6 | 3, 5 | rspc 3111 |
. 2
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7 | rspc2.2 |
. . 3
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8 | rspc2.4 |
. . 3
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9 | 7, 8 | rspc 3111 |
. 2
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10 | 6, 9 | sylan9 667 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ral 2741 df-v 3014 |
This theorem is referenced by: rspc2v 3126 reu2eqd 3202 fvmpt2curryd 7004 dvmptfsum 22938 poimirlem26 31967 fphpd 35660 |
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