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Mirrors > Home > MPE Home > Th. List > sbcralt | Structured version Visualization version Unicode version |
Description: Interchange class substitution and restricted quantifier. (Contributed by NM, 1-Mar-2008.) (Revised by David Abernethy, 22-Feb-2010.) |
Ref | Expression |
---|---|
sbcralt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcco 3301 |
. 2
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2 | simpl 463 |
. . 3
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3 | sbsbc 3282 |
. . . . 5
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4 | nfcv 2602 |
. . . . . . 7
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5 | nfs1v 2276 |
. . . . . . 7
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6 | 4, 5 | nfral 2785 |
. . . . . 6
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7 | sbequ12 2093 |
. . . . . . 7
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8 | 7 | ralbidv 2838 |
. . . . . 6
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9 | 6, 8 | sbie 2247 |
. . . . 5
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10 | 3, 9 | bitr3i 259 |
. . . 4
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11 | nfnfc1 2605 |
. . . . . . 7
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12 | nfcvd 2603 |
. . . . . . . 8
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13 | id 22 |
. . . . . . . 8
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14 | 12, 13 | nfeqd 2609 |
. . . . . . 7
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15 | 11, 14 | nfan1 2020 |
. . . . . 6
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16 | dfsbcq2 3281 |
. . . . . . 7
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17 | 16 | adantl 472 |
. . . . . 6
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18 | 15, 17 | ralbid 2833 |
. . . . 5
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19 | 18 | adantll 725 |
. . . 4
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20 | 10, 19 | syl5bb 265 |
. . 3
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21 | 2, 20 | sbcied 3315 |
. 2
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22 | 1, 21 | syl5bbr 267 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ral 2753 df-v 3058 df-sbc 3279 |
This theorem is referenced by: sbcrext 3352 sbcralg 3353 |
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