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Mirrors > Home > MPE Home > Th. List > nfcdeq | Structured version Visualization version Unicode version |
Description: If we have a conditional equality proof, where is and is , and in fact does not have free in it according to , then unconditionally. This proves that is actually a not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfcdeq.1 | |
nfcdeq.2 | CondEq |
Ref | Expression |
---|---|
nfcdeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcdeq.1 | . . 3 | |
2 | 1 | sbf 2380 | . 2 |
3 | nfv 1843 | . . 3 | |
4 | nfcdeq.2 | . . . 4 CondEq | |
5 | 4 | cdeqri 3421 | . . 3 |
6 | 3, 5 | sbie 2408 | . 2 |
7 | 2, 6 | bitr3i 266 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wnf 1708 wsb 1880 CondEqwcdeq 3418 |
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 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-sb 1881 df-cdeq 3419 |
This theorem is referenced by: nfccdeq 3433 |
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