Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > afvfundmfveq | Structured version Visualization version Unicode version |
Description: If a class is a function restricted to a member of its domain, then the function value for this member is equal for both definitions. (Contributed by Alexander van der Vekens, 25-May-2017.) |
Ref | Expression |
---|---|
afvfundmfveq | defAt ''' |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfafv2 41212 | . 2 ''' defAt | |
2 | iftrue 4092 | . 2 defAt defAt | |
3 | 1, 2 | syl5eq 2668 | 1 defAt ''' |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 cvv 3200 cif 4086 cfv 5888 defAt wdfat 41193 '''cafv 41194 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-un 3579 df-if 4087 df-fv 5896 df-afv 41197 |
This theorem is referenced by: afvnufveq 41227 afvfvn0fveq 41230 afv0nbfvbi 41231 afveu 41233 fnbrafvb 41234 afvelrn 41248 afvres 41252 tz6.12-afv 41253 dmfcoafv 41255 afvco2 41256 rlimdmafv 41257 aovfundmoveq 41261 |
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