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Mirrors > Home > HOLE Home > Th. List > insti | GIF version |
Description: Instantiate a theorem with a new term. |
Ref | Expression |
---|---|
insti.1 | ⊢ C:α |
insti.2 | ⊢ B:∗ |
insti.3 | ⊢ R⊧A |
insti.4 | ⊢ ⊤⊧[(λx:α By:α) = B] |
insti.5 | ⊢ [x:α = C]⊧[A = B] |
Ref | Expression |
---|---|
insti | ⊢ R⊧B |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | insti.3 | . 2 ⊢ R⊧A | |
2 | insti.4 | . 2 ⊢ ⊤⊧[(λx:α By:α) = B] | |
3 | 1 | ax-cb1 29 | . . 3 ⊢ R:∗ |
4 | wv 58 | . . 3 ⊢ y:α:α | |
5 | 3, 4 | ax-17 95 | . 2 ⊢ ⊤⊧[(λx:α Ry:α) = R] |
6 | insti.5 | . 2 ⊢ [x:α = C]⊧[A = B] | |
7 | 6 | ax-cb1 29 | . . 3 ⊢ [x:α = C]:∗ |
8 | 7, 3 | eqid 73 | . 2 ⊢ [x:α = C]⊧[R = R] |
9 | 1, 2, 5, 6, 8 | ax-inst 103 | 1 ⊢ R⊧B |
Colors of variables: type var term |
Syntax hints: tv 1 ∗hb 3 kc 5 λkl 6 = ke 7 ⊤kt 8 [kbr 9 ⊧wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ceq 46 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: clf 105 exlimdv 157 cbvf 167 exlimd 171 |
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