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Mirrors > Home > HOLE Home > Th. List > imp | GIF version |
Description: Importation deduction. |
Ref | Expression |
---|---|
imp.1 | ⊢ S:∗ |
imp.2 | ⊢ T:∗ |
imp.3 | ⊢ R⊧[S ⇒ T] |
Ref | Expression |
---|---|
imp | ⊢ (R, S)⊧T |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp.2 | . 2 ⊢ T:∗ | |
2 | imp.3 | . . . 4 ⊢ R⊧[S ⇒ T] | |
3 | 2 | ax-cb1 29 | . . 3 ⊢ R:∗ |
4 | imp.1 | . . 3 ⊢ S:∗ | |
5 | 3, 4 | simpr 23 | . 2 ⊢ (R, S)⊧S |
6 | 2, 4 | adantr 50 | . 2 ⊢ (R, S)⊧[S ⇒ T] |
7 | 1, 5, 6 | mpd 146 | 1 ⊢ (R, S)⊧T |
Colors of variables: type var term |
Syntax hints: ∗hb 3 [kbr 9 kct 10 ⊧wffMMJ2 11 wffMMJ2t 12 ⇒ tim 111 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 df-an 118 df-im 119 |
This theorem is referenced by: con2d 151 exlimdv 157 alnex 174 notnot 187 ax3 192 |
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