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Mirrors > Home > MPE Home > Th. List > nfrecs | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.) |
Ref | Expression |
---|---|
nfrecs.f | ⊢ Ⅎ𝑥𝐹 |
Ref | Expression |
---|---|
nfrecs | ⊢ Ⅎ𝑥recs(𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-recs 7991 | . 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹) | |
2 | nfcv 2955 | . . 3 ⊢ Ⅎ𝑥 E | |
3 | nfcv 2955 | . . 3 ⊢ Ⅎ𝑥On | |
4 | nfrecs.f | . . 3 ⊢ Ⅎ𝑥𝐹 | |
5 | 2, 3, 4 | nfwrecs 7932 | . 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹) |
6 | 1, 5 | nfcxfr 2953 | 1 ⊢ Ⅎ𝑥recs(𝐹) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2936 E cep 5429 Oncon0 6159 wrecscwrecs 7929 recscrecs 7990 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ral 3111 df-rex 3112 df-rab 3115 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-uni 4801 df-br 5031 df-opab 5093 df-xp 5525 df-cnv 5527 df-dm 5529 df-rn 5530 df-res 5531 df-ima 5532 df-pred 6116 df-iota 6283 df-fv 6332 df-wrecs 7930 df-recs 7991 |
This theorem is referenced by: nfrdg 8033 nfoi 8962 aomclem8 40005 |
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