Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-lem-moexsb | Structured version Visualization version Unicode version |
Description: The antecedent
relates to
, but is
better suited for usage in proofs. Note that no distinct variable
restriction is placed on .
This theorem provides a basic working step in proving theorems about or . (Contributed by Wolf Lammen, 3-Oct-2019.) |
Ref | Expression |
---|---|
wl-lem-moexsb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2028 | . . 3 | |
2 | nfs1v 2437 | . . 3 | |
3 | sp 2053 | . . . . 5 | |
4 | ax12v2 2049 | . . . . 5 | |
5 | 3, 4 | syli 39 | . . . 4 |
6 | sb2 2352 | . . . 4 | |
7 | 5, 6 | syl6 35 | . . 3 |
8 | 1, 2, 7 | exlimd 2087 | . 2 |
9 | spsbe 1884 | . 2 | |
10 | 8, 9 | impbid1 215 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wex 1704 wsb 1880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-sb 1881 |
This theorem is referenced by: (None) |
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