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Mirrors > Home > NFE Home > Th. List > nfae | GIF version |
Description: All variables are effectively bound in an identical variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfae | ⊢ Ⅎz∀x x = y |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbae 1953 | . 2 ⊢ (∀x x = y → ∀z∀x x = y) | |
2 | 1 | nfi 1551 | 1 ⊢ Ⅎz∀x x = y |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1540 Ⅎwnf 1544 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: nfnae 1956 sbequ5 2031 a16nf 2051 sbcom 2089 sbcom2 2114 exists1 2293 copsexg 4607 |
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