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Mirrors > Home > MPE Home > Th. List > rspcedeq1vd | Structured version Visualization version Unicode version |
Description: Restricted existential specialization, using implicit substitution. Variant of rspcedvd 3317 for equations, in which the left hand side depends on the quantified variable. (Contributed by AV, 24-Dec-2019.) |
Ref | Expression |
---|---|
rspcedeqvd.1 | |
rspcedeqvd.2 |
Ref | Expression |
---|---|
rspcedeq1vd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspcedeqvd.1 | . 2 | |
2 | rspcedeqvd.2 | . . 3 | |
3 | 2 | eqeq1d 2624 | . 2 |
4 | eqidd 2623 | . 2 | |
5 | 1, 3, 4 | rspcedvd 3317 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wrex 2913 |
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-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 |
This theorem is referenced by: mod2eq1n2dvds 15071 |
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