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| 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 8412 | . 2 ⊢ recs(𝐹) = wrecs( E , On, 𝐹) | |
| 2 | nfcv 2904 | . . 3 ⊢ Ⅎ𝑥 E | |
| 3 | nfcv 2904 | . . 3 ⊢ Ⅎ𝑥On | |
| 4 | nfrecs.f | . . 3 ⊢ Ⅎ𝑥𝐹 | |
| 5 | 2, 3, 4 | nfwrecs 8342 | . 2 ⊢ Ⅎ𝑥wrecs( E , On, 𝐹) | 
| 6 | 1, 5 | nfcxfr 2902 | 1 ⊢ Ⅎ𝑥recs(𝐹) | 
| Colors of variables: wff setvar class | 
| Syntax hints: Ⅎwnfc 2889 E cep 5582 Oncon0 6383 wrecscwrecs 8337 recscrecs 8411 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-10 2140 ax-11 2156 ax-12 2176 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-nf 1783 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-nfc 2891 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-dif 3953 df-un 3955 df-in 3957 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-opab 5205 df-xp 5690 df-cnv 5692 df-co 5693 df-dm 5694 df-rn 5695 df-res 5696 df-ima 5697 df-pred 6320 df-iota 6513 df-fv 6568 df-ov 7435 df-frecs 8307 df-wrecs 8338 df-recs 8412 | 
| This theorem is referenced by: nfrdg 8455 nfoi 9555 aomclem8 43078 | 
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