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Mirrors > Home > MPE Home > Th. List > dfixp | Structured version Visualization version Unicode version |
Description: Eliminate the expression in df-ixp 7909, under the assumption that and are disjoint. This way, we can say that is bound in even if it appears free in . (Contributed by Mario Carneiro, 12-Aug-2016.) |
Ref | Expression |
---|---|
dfixp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ixp 7909 | . 2 | |
2 | abid2 2745 | . . . . 5 | |
3 | 2 | fneq2i 5986 | . . . 4 |
4 | 3 | anbi1i 731 | . . 3 |
5 | 4 | abbii 2739 | . 2 |
6 | 1, 5 | eqtri 2644 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wcel 1990 cab 2608 wral 2912 wfn 5883 cfv 5888 cixp 7908 |
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-fn 5891 df-ixp 7909 |
This theorem is referenced by: ixpsnval 7911 elixp2 7912 ixpeq1 7919 cbvixp 7925 ixp0x 7936 |
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