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Mirrors > Home > MPE Home > Th. List > gencbvex | Structured version Visualization version Unicode version |
Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
gencbvex.1 | |
gencbvex.2 | |
gencbvex.3 | |
gencbvex.4 |
Ref | Expression |
---|---|
gencbvex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 2042 | . 2 | |
2 | gencbvex.1 | . . . 4 | |
3 | gencbvex.3 | . . . . . . 7 | |
4 | gencbvex.2 | . . . . . . 7 | |
5 | 3, 4 | anbi12d 747 | . . . . . 6 |
6 | 5 | bicomd 213 | . . . . 5 |
7 | 6 | eqcoms 2630 | . . . 4 |
8 | 2, 7 | ceqsexv 3242 | . . 3 |
9 | 8 | exbii 1774 | . 2 |
10 | 19.41v 1914 | . . . 4 | |
11 | simpr 477 | . . . . 5 | |
12 | gencbvex.4 | . . . . . . . 8 | |
13 | eqcom 2629 | . . . . . . . . . . 11 | |
14 | 13 | biimpi 206 | . . . . . . . . . 10 |
15 | 14 | adantl 482 | . . . . . . . . 9 |
16 | 15 | eximi 1762 | . . . . . . . 8 |
17 | 12, 16 | sylbi 207 | . . . . . . 7 |
18 | 17 | adantr 481 | . . . . . 6 |
19 | 18 | ancri 575 | . . . . 5 |
20 | 11, 19 | impbii 199 | . . . 4 |
21 | 10, 20 | bitri 264 | . . 3 |
22 | 21 | exbii 1774 | . 2 |
23 | 1, 9, 22 | 3bitr3i 290 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 cvv 3200 |
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-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-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: gencbvex2 3251 gencbval 3252 |
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