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Mirrors > Home > NFE Home > Th. List > csbresg | Unicode version |
Description: Distribute proper substitution through the restriction of a class. csbresg 4976 is derived from the virtual deduction proof csbresgVD in set.mm. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbresg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbing 3462 | . . 3 | |
2 | csbxpg 4813 | . . . . 5 | |
3 | csbconstg 3150 | . . . . . 6 | |
4 | 3 | xpeq2d 4808 | . . . . 5 |
5 | 2, 4 | eqtrd 2385 | . . . 4 |
6 | 5 | ineq2d 3457 | . . 3 |
7 | 1, 6 | eqtrd 2385 | . 2 |
8 | df-res 4788 | . . 3 | |
9 | 8 | csbeq2i 3162 | . 2 |
10 | df-res 4788 | . 2 | |
11 | 7, 9, 10 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 wcel 1710 cvv 2859 csb 3136 cin 3208 cxp 4770 cres 4774 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-sbc 3047 df-csb 3137 df-nin 3211 df-compl 3212 df-in 3213 df-opab 4623 df-xp 4784 df-res 4788 |
This theorem is referenced by: (None) |
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