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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 1528 | . 2 | |
2 | nfa2 1566 | . 2 | |
3 | sp 1498 | . . . . 5 | |
4 | 3 | sps 1524 | . . . 4 |
5 | cbv1h.1 | . . . 4 | |
6 | 4, 5 | syl 14 | . . 3 |
7 | 2, 6 | nfd 1510 | . 2 |
8 | cbv1h.2 | . . . 4 | |
9 | 4, 8 | syl 14 | . . 3 |
10 | 1, 9 | nfd 1510 | . 2 |
11 | cbv1h.3 | . . 3 | |
12 | 4, 11 | syl 14 | . 2 |
13 | 1, 2, 7, 10, 12 | cbv1 1732 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-nf 1448 |
This theorem is referenced by: cbv2h 1735 |
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