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Mirrors > Home > NFE Home > Th. List > gencbvex | 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 |
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gencbvex.1 | |
gencbvex.2 | |
gencbvex.3 | |
gencbvex.4 |
Ref | Expression |
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gencbvex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1741 | . 2 | |
2 | gencbvex.1 | . . . 4 | |
3 | gencbvex.3 | . . . . . . 7 | |
4 | gencbvex.2 | . . . . . . 7 | |
5 | 3, 4 | anbi12d 691 | . . . . . 6 |
6 | 5 | bicomd 192 | . . . . 5 |
7 | 6 | eqcoms 2356 | . . . 4 |
8 | 2, 7 | ceqsexv 2894 | . . 3 |
9 | 8 | exbii 1582 | . 2 |
10 | 19.41v 1901 | . . . 4 | |
11 | simpr 447 | . . . . 5 | |
12 | gencbvex.4 | . . . . . . . 8 | |
13 | eqcom 2355 | . . . . . . . . . . 11 | |
14 | 13 | biimpi 186 | . . . . . . . . . 10 |
15 | 14 | adantl 452 | . . . . . . . . 9 |
16 | 15 | eximi 1576 | . . . . . . . 8 |
17 | 12, 16 | sylbi 187 | . . . . . . 7 |
18 | 17 | adantr 451 | . . . . . 6 |
19 | 18 | ancri 535 | . . . . 5 |
20 | 11, 19 | impbii 180 | . . . 4 |
21 | 10, 20 | bitri 240 | . . 3 |
22 | 21 | exbii 1582 | . 2 |
23 | 1, 9, 22 | 3bitr3i 266 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wceq 1642 wcel 1710 cvv 2859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: gencbvex2 2902 gencbval 2903 |
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