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Mirrors > Home > MPE Home > Th. List > csbiedf | Structured version Visualization version Unicode version |
Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
csbiedf.1 | |
csbiedf.2 | |
csbiedf.3 | |
csbiedf.4 |
Ref | Expression |
---|---|
csbiedf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbiedf.1 | . . 3 | |
2 | csbiedf.4 | . . . 4 | |
3 | 2 | ex 450 | . . 3 |
4 | 1, 3 | alrimi 2082 | . 2 |
5 | csbiedf.3 | . . 3 | |
6 | csbiedf.2 | . . 3 | |
7 | csbiebt 3553 | . . 3 | |
8 | 5, 6, 7 | syl2anc 693 | . 2 |
9 | 4, 8 | mpbid 222 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wceq 1483 wnf 1708 wcel 1990 wnfc 2751 csb 3533 |
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-11 2034 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-nfc 2753 df-v 3202 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: csbied 3560 csbie2t 3562 fprodsplit1f 14721 natpropd 16636 fucpropd 16637 gsummptf1o 18362 gsummpt2d 29781 sumsnd 39185 fsumsplit1 39804 |
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