Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > nfrecs | Structured version Visualization version Unicode version |
Description: Bound-variable hypothesis builder for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.) |
Ref | Expression |
---|---|
nfrecs.f |
Ref | Expression |
---|---|
nfrecs | recs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-recs 7468 | . 2 recs wrecs | |
2 | nfcv 2764 | . . 3 | |
3 | nfcv 2764 | . . 3 | |
4 | nfrecs.f | . . 3 | |
5 | 2, 3, 4 | nfwrecs 7409 | . 2 wrecs |
6 | 1, 5 | nfcxfr 2762 | 1 recs |
Colors of variables: wff setvar class |
Syntax hints: wnfc 2751 cep 5028 con0 5723 wrecscwrecs 7406 recscrecs 7467 |
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-3an 1039 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-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 df-iota 5851 df-fv 5896 df-wrecs 7407 df-recs 7468 |
This theorem is referenced by: nfrdg 7510 nfoi 8419 aomclem8 37631 |
Copyright terms: Public domain | W3C validator |