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Mirrors > Home > ILE Home > Th. List > csbima12g | Unicode version |
Description: Move class substitution in and out of the image of a function. (Contributed by FL, 15-Dec-2006.) (Proof shortened by Mario Carneiro, 4-Dec-2016.) |
Ref | Expression |
---|---|
csbima12g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3074 |
. . 3
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2 | csbeq1 3074 |
. . . 4
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3 | csbeq1 3074 |
. . . 4
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4 | 2, 3 | imaeq12d 4985 |
. . 3
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5 | 1, 4 | eqeq12d 2203 |
. 2
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6 | vex 2754 |
. . 3
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7 | nfcsb1v 3104 |
. . . 4
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8 | nfcsb1v 3104 |
. . . 4
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9 | 7, 8 | nfima 4992 |
. . 3
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10 | csbeq1a 3080 |
. . . 4
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11 | csbeq1a 3080 |
. . . 4
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12 | 10, 11 | imaeq12d 4985 |
. . 3
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13 | 6, 9, 12 | csbief 3115 |
. 2
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14 | 5, 13 | vtoclg 2811 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-rab 2476 df-v 2753 df-sbc 2977 df-csb 3072 df-un 3147 df-in 3149 df-ss 3156 df-sn 3612 df-pr 3613 df-op 3615 df-br 4018 df-opab 4079 df-xp 4646 df-cnv 4648 df-dm 4650 df-rn 4651 df-res 4652 df-ima 4653 |
This theorem is referenced by: (None) |
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