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Mirrors > Home > MPE Home > Th. List > cbvopab2 | Structured version Visualization version Unicode version |
Description: Change second bound variable in an ordered-pair class abstraction, using explicit substitution. (Contributed by NM, 22-Aug-2013.) |
Ref | Expression |
---|---|
cbvopab2.1 |
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cbvopab2.2 |
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cbvopab2.3 |
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Ref | Expression |
---|---|
cbvopab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1772 |
. . . . . 6
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2 | cbvopab2.1 |
. . . . . 6
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3 | 1, 2 | nfan 2022 |
. . . . 5
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4 | nfv 1772 |
. . . . . 6
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5 | cbvopab2.2 |
. . . . . 6
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6 | 4, 5 | nfan 2022 |
. . . . 5
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7 | opeq2 4181 |
. . . . . . 7
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8 | 7 | eqeq2d 2472 |
. . . . . 6
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9 | cbvopab2.3 |
. . . . . 6
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10 | 8, 9 | anbi12d 722 |
. . . . 5
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11 | 3, 6, 10 | cbvex 2126 |
. . . 4
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12 | 11 | exbii 1729 |
. . 3
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13 | 12 | abbii 2578 |
. 2
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14 | df-opab 4478 |
. 2
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15 | df-opab 4478 |
. 2
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16 | 13, 14, 15 | 3eqtr4i 2494 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-opab 4478 |
This theorem is referenced by: cbvoprab3 6399 |
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