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Mirrors > Home > MPE Home > Th. List > freq2 | Structured version Visualization version Unicode version |
Description: Equality theorem for the well-founded predicate. (Contributed by NM, 3-Apr-1994.) |
Ref | Expression |
---|---|
freq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss2 3658 | . . 3 | |
2 | frss 5081 | . . 3 | |
3 | 1, 2 | syl 17 | . 2 |
4 | eqimss 3657 | . . 3 | |
5 | frss 5081 | . . 3 | |
6 | 4, 5 | syl 17 | . 2 |
7 | 3, 6 | impbid 202 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wss 3574 wfr 5070 |
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-in 3581 df-ss 3588 df-fr 5073 |
This theorem is referenced by: weeq2 5103 frsn 5189 f1oweALT 7152 frfi 8205 freq12d 37609 ifr0 38654 |
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