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Mirrors > Home > MPE Home > Th. List > dffun3 | Structured version Visualization version Unicode version |
Description: Alternate definition of function. (Contributed by NM, 29-Dec-1996.) |
Ref | Expression |
---|---|
dffun3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun2 5610 |
. 2
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2 | breq2 4419 |
. . . . . 6
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3 | 2 | mo4 2356 |
. . . . 5
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4 | mo2v 2316 |
. . . . 5
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5 | 3, 4 | bitr3i 259 |
. . . 4
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6 | 5 | albii 1701 |
. . 3
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7 | 6 | anbi2i 705 |
. 2
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8 | 1, 7 | bitri 257 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pr 4652 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rab 2757 df-v 3058 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-br 4416 df-opab 4475 df-id 4767 df-cnv 4860 df-co 4861 df-fun 5602 |
This theorem is referenced by: dffun5 5613 dffun6f 5614 sbcfung 5623 dffv2 5960 |
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