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Mirrors > Home > MPE Home > Th. List > dff4 | Structured version Unicode version |
Description: Alternate definition of a mapping. (Contributed by NM, 20-Mar-2007.) |
Ref | Expression |
---|---|
dff4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dff3 5968 |
. 2
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2 | df-br 4404 |
. . . . . . . 8
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3 | ssel 3461 |
. . . . . . . . 9
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4 | opelxp2 4984 |
. . . . . . . . 9
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5 | 3, 4 | syl6 33 |
. . . . . . . 8
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6 | 2, 5 | syl5bi 217 |
. . . . . . 7
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7 | 6 | pm4.71rd 635 |
. . . . . 6
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8 | 7 | eubidv 2285 |
. . . . 5
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9 | df-reu 2806 |
. . . . 5
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10 | 8, 9 | syl6bbr 263 |
. . . 4
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11 | 10 | ralbidv 2846 |
. . 3
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12 | 11 | pm5.32i 637 |
. 2
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13 | 1, 12 | bitri 249 |
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-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4524 ax-nul 4532 ax-pr 4642 |
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-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-reu 2806 df-rab 2808 df-v 3080 df-sbc 3295 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-sn 3989 df-pr 3991 df-op 3995 df-uni 4203 df-br 4404 df-opab 4462 df-id 4747 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-fv 5537 |
This theorem is referenced by: exfo 5973 |
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