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Mirrors > Home > MPE Home > Th. List > seqeq2 | Structured version Unicode version |
Description: Equality theorem for the sequence builder operation. (Contributed by Mario Carneiro, 4-Sep-2013.) |
Ref | Expression |
---|---|
seqeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqidd 2452 |
. . . . 5
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2 | oveq 6198 |
. . . . . 6
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3 | 2 | opeq2d 4166 |
. . . . 5
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4 | 1, 1, 3 | mpt2eq123dv 6249 |
. . . 4
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5 | rdgeq1 6969 |
. . . 4
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6 | 4, 5 | syl 16 |
. . 3
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7 | 6 | imaeq1d 5268 |
. 2
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8 | df-seq 11910 |
. 2
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9 | df-seq 11910 |
. 2
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10 | 7, 8, 9 | 3eqtr4g 2517 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3072 df-dif 3431 df-un 3433 df-in 3435 df-ss 3442 df-nul 3738 df-if 3892 df-sn 3978 df-pr 3980 df-op 3984 df-uni 4192 df-br 4393 df-opab 4451 df-mpt 4452 df-cnv 4948 df-dm 4950 df-rn 4951 df-res 4952 df-ima 4953 df-iota 5481 df-fv 5526 df-ov 6195 df-oprab 6196 df-mpt2 6197 df-recs 6934 df-rdg 6968 df-seq 11910 |
This theorem is referenced by: seqeq2d 11916 sadcom 13763 gxfval 23881 ressmulgnn 26280 cvmliftlem15 27323 |
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