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Mirrors > Home > MPE Home > Th. List > sbcrel | Structured version Visualization version Unicode version |
Description: Distribute proper substitution through a relation predicate. (Contributed by Alexander van der Vekens, 23-Jul-2017.) |
Ref | Expression |
---|---|
sbcrel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcssg 4085 | . . 3 | |
2 | csbconstg 3546 | . . . 4 | |
3 | 2 | sseq2d 3633 | . . 3 |
4 | 1, 3 | bitrd 268 | . 2 |
5 | df-rel 5121 | . . 3 | |
6 | 5 | sbcbii 3491 | . 2 |
7 | df-rel 5121 | . 2 | |
8 | 4, 6, 7 | 3bitr4g 303 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wcel 1990 cvv 3200 wsbc 3435 csb 3533 wss 3574 cxp 5112 wrel 5119 |
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-tru 1486 df-fal 1489 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 df-dif 3577 df-in 3581 df-ss 3588 df-nul 3916 df-rel 5121 |
This theorem is referenced by: sbcfung 5912 |
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