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Mirrors > Home > NFE Home > Th. List > sban | Unicode version |
Description: Conjunction inside and outside of a substitution are equivalent. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sban |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbn 2062 | . . 3 | |
2 | sbim 2065 | . . . 4 | |
3 | sbn 2062 | . . . . 5 | |
4 | 3 | imbi2i 303 | . . . 4 |
5 | 2, 4 | bitri 240 | . . 3 |
6 | 1, 5 | xchbinx 301 | . 2 |
7 | df-an 360 | . . 3 | |
8 | 7 | sbbii 1653 | . 2 |
9 | df-an 360 | . 2 | |
10 | 6, 8, 9 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wa 358 wsb 1648 |
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 df-sb 1649 |
This theorem is referenced by: sb3an 2070 sbbi 2071 sbabel 2515 cbvreu 2833 sbcan 3088 sbcang 3089 rmo3 3133 inab 3522 difab 3523 |
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