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Mirrors > Home > MPE Home > Th. List > iineq1 | Structured version Visualization version Unicode version |
Description: Equality theorem for indexed intersection. (Contributed by NM, 27-Jun-1998.) |
Ref | Expression |
---|---|
iineq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq 2999 |
. . 3
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2 | 1 | abbidv 2580 |
. 2
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3 | df-iin 4295 |
. 2
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4 | df-iin 4295 |
. 2
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5 | 2, 3, 4 | 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-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-an 377 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-ral 2754 df-iin 4295 |
This theorem is referenced by: iinrab2 4355 iinvdif 4364 riin0 4366 iin0 4591 xpriindi 4990 cmpfi 20472 ptbasfi 20645 fclsval 21072 taylfval 23363 polvalN 33515 |
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