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Mirrors > Home > MPE Home > Th. List > Mathboxes > ssralv2 | Structured version Visualization version Unicode version |
Description: Quantification restricted to a subclass for two quantifiers. ssralv 3666 for two quantifiers. The proof of ssralv2 38737 was automatically generated by minimizing the automatically translated proof of ssralv2VD 39102. The automatic translation is by the tools program translatewithout_overwriting.cmd. (Contributed by Alan Sare, 18-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ssralv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . 2 | |
2 | nfra1 2941 | . 2 | |
3 | ssralv 3666 | . . . . . 6 | |
4 | 3 | adantr 481 | . . . . 5 |
5 | df-ral 2917 | . . . . 5 | |
6 | 4, 5 | syl6ib 241 | . . . 4 |
7 | sp 2053 | . . . 4 | |
8 | 6, 7 | syl6 35 | . . 3 |
9 | ssralv 3666 | . . . 4 | |
10 | 9 | adantl 482 | . . 3 |
11 | 8, 10 | syl6d 75 | . 2 |
12 | 1, 2, 11 | ralrimd 2959 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wcel 1990 wral 2912 wss 3574 |
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-ral 2917 df-in 3581 df-ss 3588 |
This theorem is referenced by: ordelordALT 38747 ordelordALTVD 39103 |
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