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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > csbfv12gALTOLD | Structured version Visualization version Unicode version |
Description: Move class substitution in and out of a function value. The proof is derived from the virtual deduction proof csbfv12gALTVD 37337. (Contributed by Alan Sare, 10-Nov-2012.) Obsolete as of 20-Aug-2018. Use csbfv12 5927 instead. (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
csbfv12gALTOLD |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbunigOLD 37253 |
. . 3
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2 | csbabgOLD 37252 |
. . . . 5
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3 | sbceqg 3785 |
. . . . . . 7
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4 | csbima12gOLD 5208 |
. . . . . . . . 9
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5 | csbsng 4042 |
. . . . . . . . . 10
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6 | 5 | imaeq2d 5190 |
. . . . . . . . 9
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7 | 4, 6 | eqtrd 2496 |
. . . . . . . 8
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8 | csbconstg 3388 |
. . . . . . . 8
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9 | 7, 8 | eqeq12d 2477 |
. . . . . . 7
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10 | 3, 9 | bitrd 261 |
. . . . . 6
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11 | 10 | abbidv 2580 |
. . . . 5
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12 | 2, 11 | eqtrd 2496 |
. . . 4
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13 | 12 | unieqd 4222 |
. . 3
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14 | 1, 13 | eqtrd 2496 |
. 2
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15 | dffv4 5889 |
. . 3
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16 | 15 | csbeq2i 3794 |
. 2
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17 | dffv4 5889 |
. 2
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18 | 14, 16, 17 | 3eqtr4g 2521 |
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-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-fal 1461 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 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-uni 4213 df-br 4419 df-opab 4478 df-xp 4862 df-cnv 4864 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fv 5613 |
This theorem is referenced by: (None) |
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