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Mirrors > Home > MPE Home > Th. List > sbc2iedv | Structured version Visualization version Unicode version |
Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 16-Dec-2008.) (Proof shortened by Mario Carneiro, 18-Oct-2016.) |
Ref | Expression |
---|---|
sbc2iedv.1 | |
sbc2iedv.2 | |
sbc2iedv.3 |
Ref | Expression |
---|---|
sbc2iedv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc2iedv.1 | . . 3 | |
2 | 1 | a1i 11 | . 2 |
3 | sbc2iedv.2 | . . . 4 | |
4 | 3 | a1i 11 | . . 3 |
5 | sbc2iedv.3 | . . . 4 | |
6 | 5 | impl 650 | . . 3 |
7 | 4, 6 | sbcied 3472 | . 2 |
8 | 2, 7 | sbcied 3472 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 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: dfoprab3 7224 sbcie2s 15916 ismnddef 17296 sdclem1 33539 |
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