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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 8410 | . 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹) | |
2 | nfcv 2903 | . . 3 ⊢ Ⅎ𝑥 E | |
3 | nfcv 2903 | . . 3 ⊢ Ⅎ𝑥On | |
4 | nfrecs.f | . . 3 ⊢ Ⅎ𝑥𝐹 | |
5 | 2, 3, 4 | nfwrecs 8340 | . 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹) |
6 | 1, 5 | nfcxfr 2901 | 1 ⊢ Ⅎ𝑥recs(𝐹) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2888 E cep 5588 Oncon0 6386 wrecscwrecs 8335 recscrecs 8409 |
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 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-nf 1781 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-ral 3060 df-rex 3069 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-in 3970 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-br 5149 df-opab 5211 df-xp 5695 df-cnv 5697 df-co 5698 df-dm 5699 df-rn 5700 df-res 5701 df-ima 5702 df-pred 6323 df-iota 6516 df-fv 6571 df-ov 7434 df-frecs 8305 df-wrecs 8336 df-recs 8410 |
This theorem is referenced by: nfrdg 8453 nfoi 9552 aomclem8 43050 |
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