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Mirrors > Home > NFE Home > Th. List > sb56 | Unicode version |
Description: Two equivalent ways of expressing the proper substitution of for in , when and are distinct. Theorem 6.2 of [Quine] p. 40. The proof does not involve df-sb 1649. (Contributed by NM, 14-Apr-2008.) |
Ref | Expression |
---|---|
sb56 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1788 | . 2 | |
2 | ax11v 2096 | . . 3 | |
3 | sp 1747 | . . . 4 | |
4 | 3 | com12 27 | . . 3 |
5 | 2, 4 | impbid 183 | . 2 |
6 | 1, 5 | equsex 1962 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wal 1540 wex 1541 |
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-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: sb6 2099 sb5 2100 alexeq 2968 |
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