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Mirrors > Home > MPE Home > Th. List > sbc3ie | Structured version Visualization version Unicode version |
Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Mario Carneiro, 19-Jun-2014.) (Revised by Mario Carneiro, 29-Dec-2014.) |
Ref | Expression |
---|---|
sbc3ie.1 | |
sbc3ie.2 | |
sbc3ie.3 | |
sbc3ie.4 |
Ref | Expression |
---|---|
sbc3ie |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc3ie.1 | . 2 | |
2 | sbc3ie.2 | . 2 | |
3 | sbc3ie.3 | . . . 4 | |
4 | 3 | a1i 11 | . . 3 |
5 | sbc3ie.4 | . . . 4 | |
6 | 5 | 3expa 1265 | . . 3 |
7 | 4, 6 | sbcied 3472 | . 2 |
8 | 1, 2, 7 | sbc2ie 3505 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 cvv 3200 wsbc 3435 |
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-9 1999 ax-10 2019 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 df-sbc 3436 |
This theorem is referenced by: isdlat 17193 islmod 18867 isslmd 29755 hdmap1fval 37086 hdmapfval 37119 hgmapfval 37178 rmydioph 37581 |
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