Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ralimralim | Structured version Visualization version Unicode version |
Description: Introducing any antecedent in a restricted universal quantification. (Contributed by Glauco Siliprandi, 3-Mar-2021.) |
Ref | Expression |
---|---|
ralimralim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2941 | . 2 | |
2 | rspa 2930 | . . . 4 | |
3 | ax-1 6 | . . . 4 | |
4 | 2, 3 | syl 17 | . . 3 |
5 | 4 | ex 450 | . 2 |
6 | 1, 5 | ralrimi 2957 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 wral 2912 |
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-10 2019 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-ral 2917 |
This theorem is referenced by: infxrunb2 39584 |
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