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Mirrors > Home > NFE Home > Th. List > sbralie | Unicode version |
Description: Implicit to explicit substitution that swaps variables in a quantified expression. (Contributed by NM, 5-Sep-2004.) |
Ref | Expression |
---|---|
sbralie.1 |
Ref | Expression |
---|---|
sbralie |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralsv 2846 | . . . 4 | |
2 | 1 | sbbii 1653 | . . 3 |
3 | nfv 1619 | . . . 4 | |
4 | raleq 2807 | . . . 4 | |
5 | 3, 4 | sbie 2038 | . . 3 |
6 | 2, 5 | bitri 240 | . 2 |
7 | cbvralsv 2846 | . . 3 | |
8 | nfv 1619 | . . . . . 6 | |
9 | 8 | sbco2 2086 | . . . . 5 |
10 | nfv 1619 | . . . . . 6 | |
11 | sbralie.1 | . . . . . 6 | |
12 | 10, 11 | sbie 2038 | . . . . 5 |
13 | 9, 12 | bitri 240 | . . . 4 |
14 | 13 | ralbii 2638 | . . 3 |
15 | 7, 14 | bitri 240 | . 2 |
16 | 6, 15 | bitri 240 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wsb 1648 wral 2614 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 |
This theorem is referenced by: (None) |
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