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Mirrors > Home > MPE Home > Th. List > sbcreu | Structured version Visualization version Unicode version |
Description: Interchange class substitution and restricted uniqueness quantifier. (Contributed by NM, 24-Feb-2013.) (Revised by NM, 18-Aug-2018.) |
Ref | Expression |
---|---|
sbcreu |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 3277 |
. 2
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2 | reurex 3009 |
. . 3
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3 | sbcex 3277 |
. . . 4
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4 | 3 | rexlimivw 2876 |
. . 3
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5 | 2, 4 | syl 17 |
. 2
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6 | dfsbcq2 3270 |
. . 3
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7 | dfsbcq2 3270 |
. . . 4
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8 | 7 | reubidv 2975 |
. . 3
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9 | nfcv 2592 |
. . . . 5
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10 | nfs1v 2266 |
. . . . 5
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11 | 9, 10 | nfreu 2965 |
. . . 4
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12 | sbequ12 2083 |
. . . . 5
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13 | 12 | reubidv 2975 |
. . . 4
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14 | 11, 13 | sbie 2237 |
. . 3
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15 | 6, 8, 14 | vtoclbg 3108 |
. 2
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16 | 1, 5, 15 | pm5.21nii 355 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ral 2742 df-rex 2743 df-reu 2744 df-rmo 2745 df-v 3047 df-sbc 3268 |
This theorem is referenced by: (None) |
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