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Mirrors > Home > MPE Home > Th. List > raleqbidva | Structured version Visualization version Unicode version |
Description: Equality deduction for restricted universal quantifier. (Contributed by Mario Carneiro, 5-Jan-2017.) |
Ref | Expression |
---|---|
raleqbidva.1 | |
raleqbidva.2 |
Ref | Expression |
---|---|
raleqbidva |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleqbidva.2 | . . 3 | |
2 | 1 | ralbidva 2985 | . 2 |
3 | raleqbidva.1 | . . 3 | |
4 | 3 | raleqdv 3144 | . 2 |
5 | 2, 4 | bitrd 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 |
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-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-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 |
This theorem is referenced by: catpropd 16369 cidpropd 16370 funcpropd 16560 fullpropd 16580 natpropd 16636 gsumpropd2lem 17273 istrkgc 25353 istrkgb 25354 istrkgcb 25355 istrkge 25356 iscgrg 25407 isperp 25607 clwlkclwwlk 26903 rngurd 29788 matunitlindflem1 33405 |
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