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Mirrors > Home > MPE Home > Th. List > sbhypf | Unicode version |
Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf 3453. (Contributed by Raph Levien, 10-Apr-2004.) |
Ref | Expression |
---|---|
sbhypf.1 | |
sbhypf.2 |
Ref | Expression |
---|---|
sbhypf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3112 | . . 3 | |
2 | eqeq1 2461 | . . 3 | |
3 | 1, 2 | ceqsexv 3146 | . 2 |
4 | nfs1v 2181 | . . . 4 | |
5 | sbhypf.1 | . . . 4 | |
6 | 4, 5 | nfbi 1934 | . . 3 |
7 | sbequ12 1992 | . . . . 5 | |
8 | 7 | bicomd 201 | . . . 4 |
9 | sbhypf.2 | . . . 4 | |
10 | 8, 9 | sylan9bb 699 | . . 3 |
11 | 6, 10 | exlimi 1912 | . 2 |
12 | 3, 11 | sylbir 213 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 <-> wb 184
/\ wa 369 = wceq 1395 E. wex 1612
F/ wnf 1616 [ wsb 1739 |
This theorem is referenced by: mob2 3279 reu2eqd 3296 ralxpf 5154 tfisi 6693 ac6sf 8890 nn0ind-raph 10989 cbvmptf 27494 nn0min 27611 ac6gf 30223 fdc1 30239 |
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-10 1837 ax-12 1854 ax-13 1999 ax-ext 2435 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-clab 2443 df-cleq 2449 df-clel 2452 df-v 3111 |
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