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Mirrors > Home > MPE Home > Th. List > rexxfrd | Structured version Visualization version Unicode version |
Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by FL, 10-Apr-2007.) (Revised by Mario Carneiro, 15-Aug-2014.) |
Ref | Expression |
---|---|
ralxfrd.1 | |
ralxfrd.2 | |
ralxfrd.3 |
Ref | Expression |
---|---|
rexxfrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralxfrd.1 | . . . 4 | |
2 | ralxfrd.2 | . . . 4 | |
3 | ralxfrd.3 | . . . . 5 | |
4 | 3 | notbid 308 | . . . 4 |
5 | 1, 2, 4 | ralxfrd 4879 | . . 3 |
6 | 5 | notbid 308 | . 2 |
7 | dfrex2 2996 | . 2 | |
8 | dfrex2 2996 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 303 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 |
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-ral 2917 df-rex 2918 df-v 3202 |
This theorem is referenced by: cmpfi 21211 elfm 21751 rlimcnp 24692 rmoxfrdOLD 29332 rmoxfrd 29333 iunrdx 29382 dvh4dimat 36727 mapdcv 36949 elrfirn 37258 fargshiftfo 41378 |
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