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Mirrors > Home > MPE Home > Th. List > cbvopab1s | Structured version Visualization version Unicode version |
Description: Change first bound variable in an ordered-pair class abstraction, using explicit substitution. (Contributed by NM, 31-Jul-2003.) |
Ref | Expression |
---|---|
cbvopab1s |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1761 |
. . . 4
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2 | nfv 1761 |
. . . . . 6
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3 | nfs1v 2266 |
. . . . . 6
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4 | 2, 3 | nfan 2011 |
. . . . 5
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5 | 4 | nfex 2031 |
. . . 4
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6 | opeq1 4166 |
. . . . . . 7
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7 | 6 | eqeq2d 2461 |
. . . . . 6
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8 | sbequ12 2083 |
. . . . . 6
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9 | 7, 8 | anbi12d 717 |
. . . . 5
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10 | 9 | exbidv 1768 |
. . . 4
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11 | 1, 5, 10 | cbvex 2115 |
. . 3
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12 | 11 | abbii 2567 |
. 2
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13 | df-opab 4462 |
. 2
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14 | df-opab 4462 |
. 2
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15 | 12, 13, 14 | 3eqtr4i 2483 |
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-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-rab 2746 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-opab 4462 |
This theorem is referenced by: (None) |
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