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Mirrors > Home > MPE Home > Th. List > axc11nlem | Unicode version |
Description: Lemma for axc11n 2049. Change bound variable in an equality. (Contributed by NM, 8-Jul-2016.) (Proof shortened by Wolf Lammen, 17-Feb-2018.) Restructure to ease either bundling, or reducing dependencies on axioms. (Revised by Wolf Lammen, 30-Nov-2019.) |
Ref | Expression |
---|---|
axc11nlem.1 |
Ref | Expression |
---|---|
axc11nlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvaev 1817 | . . 3 | |
2 | equequ2 1799 | . . . . 5 | |
3 | 2 | biimprd 223 | . . . 4 |
4 | 3 | al2imi 1636 | . . 3 |
5 | 1, 4 | syl5com 30 | . 2 |
6 | axc11nlem.1 | . . . . 5 | |
7 | 6 | spsd 1867 | . . . 4 |
8 | 7 | com12 31 | . . 3 |
9 | 8 | con1d 124 | . 2 |
10 | 5, 9 | pm2.61d 158 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -. wn 3 -> wi 4
A. wal 1393 |
This theorem is referenced by: aevlem1 1939 axc11n 2049 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-12 1854 |
This theorem depends on definitions: df-bi 185 df-ex 1613 |
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