Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > fnotaovb | Structured version Visualization version Unicode version |
Description: Equivalence of operation value and ordered triple membership, analogous to fnopfvb 6237. (Contributed by Alexander van der Vekens, 26-May-2017.) |
Ref | Expression |
---|---|
fnotaovb | (()) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 5148 | . . . 4 | |
2 | fnopafvb 41235 | . . . 4 ''' | |
3 | 1, 2 | sylan2 491 | . . 3 ''' |
4 | 3 | 3impb 1260 | . 2 ''' |
5 | df-aov 41198 | . . 3 (()) ''' | |
6 | 5 | eqeq1i 2627 | . 2 (()) ''' |
7 | df-ot 4186 | . . 3 | |
8 | 7 | eleq1i 2692 | . 2 |
9 | 4, 6, 8 | 3bitr4g 303 | 1 (()) |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 cop 4183 cotp 4185 cxp 5112 wfn 5883 '''cafv 41194 ((caov 41195 |
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-ot 4186 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-res 5126 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-dfat 41196 df-afv 41197 df-aov 41198 |
This theorem is referenced by: (None) |
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