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Mirrors > Home > MPE Home > Th. List > nfrel | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for a relation. (Contributed by NM, 31-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfrel.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfrel | ⊢ Ⅎ𝑥Rel 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rel 5121 | . 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) | |
2 | nfrel.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | nfcv 2764 | . . 3 ⊢ Ⅎ𝑥(V × V) | |
4 | 2, 3 | nfss 3596 | . 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V) |
5 | 1, 4 | nfxfr 1779 | 1 ⊢ Ⅎ𝑥Rel 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1708 Ⅎwnfc 2751 Vcvv 3200 ⊆ wss 3574 × cxp 5112 Rel wrel 5119 |
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-nfc 2753 df-ral 2917 df-in 3581 df-ss 3588 df-rel 5121 |
This theorem is referenced by: nffun 5911 |
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