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Mirrors > Home > MPE Home > Th. List > foelrn | Structured version Visualization version Unicode version |
Description: Property of a surjective function. (Contributed by Jeff Madsen, 4-Jan-2011.) |
Ref | Expression |
---|---|
foelrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffo3 6374 | . . 3 | |
2 | 1 | simprbi 480 | . 2 |
3 | eqeq1 2626 | . . . 4 | |
4 | 3 | rexbidv 3052 | . . 3 |
5 | 4 | rspccva 3308 | . 2 |
6 | 2, 5 | sylan 488 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 wf 5884 wfo 5886 cfv 5888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fo 5894 df-fv 5896 |
This theorem is referenced by: foco2 6379 foco2OLD 6380 fofinf1o 8241 fodomacn 8879 iunfictbso 8937 cff1 9080 cofsmo 9091 axcclem 9279 konigthlem 9390 tskuni 9605 fulli 16573 efgredlemc 18158 efgrelexlemb 18163 efgredeu 18165 ghmcyg 18297 znfld 19909 znrrg 19914 cygznlem3 19918 ovoliunnul 23275 lgsdchr 25080 foresf1o 29343 iunrdx 29382 crngohomfo 33805 fourierdlem20 40344 fourierdlem52 40375 fourierdlem63 40386 fourierdlem64 40387 fourierdlem65 40388 |
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