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Mirrors > Home > ILE Home > Th. List > cbv1h | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-May-2018.) |
Ref | Expression |
---|---|
cbv1h.1 | |
cbv1h.2 | |
cbv1h.3 |
Ref | Expression |
---|---|
cbv1h |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1434 | . 2 | |
2 | nfa2 1471 | . 2 | |
3 | sp 1401 | . . . . 5 | |
4 | 3 | sps 1430 | . . . 4 |
5 | cbv1h.1 | . . . 4 | |
6 | 4, 5 | syl 14 | . . 3 |
7 | 2, 6 | nfd 1416 | . 2 |
8 | cbv1h.2 | . . . 4 | |
9 | 4, 8 | syl 14 | . . 3 |
10 | 1, 9 | nfd 1416 | . 2 |
11 | cbv1h.3 | . . 3 | |
12 | 4, 11 | syl 14 | . 2 |
13 | 1, 2, 7, 10, 12 | cbv1 1632 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: cbv2h 1634 |
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