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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 5556 | . 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) | |
2 | nfrel.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | nfcv 2977 | . . 3 ⊢ Ⅎ𝑥(V × V) | |
4 | 2, 3 | nfss 3959 | . 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V) |
5 | 1, 4 | nfxfr 1849 | 1 ⊢ Ⅎ𝑥Rel 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1780 Ⅎwnfc 2961 Vcvv 3494 ⊆ wss 3935 × cxp 5547 Rel wrel 5554 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-in 3942 df-ss 3951 df-rel 5556 |
This theorem is referenced by: nffun 6372 |
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