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Mirrors > Home > MPE Home > Th. List > nfsn | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for singletons. (Contributed by NM, 14-Nov-1995.) |
Ref | Expression |
---|---|
nfsn.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfsn | ⊢ Ⅎ𝑥{𝐴} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 4554 | . 2 ⊢ {𝐴} = {𝐴, 𝐴} | |
2 | nfsn.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | 2, 2 | nfpr 4606 | . 2 ⊢ Ⅎ𝑥{𝐴, 𝐴} |
4 | 1, 3 | nfcxfr 2902 | 1 ⊢ Ⅎ𝑥{𝐴} |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2884 {csn 4541 {cpr 4543 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2158 ax-12 2175 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-ex 1788 df-nf 1792 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2886 df-v 3410 df-un 3871 df-sn 4542 df-pr 4544 |
This theorem is referenced by: nfop 4800 iunopeqop 5404 nfpred 6165 nfsuc 6284 sniota 6371 dfmpo 7870 bnj958 32633 bnj1000 32634 bnj1446 32738 bnj1447 32739 bnj1448 32740 bnj1466 32746 bnj1467 32747 nosupbnd2 33656 noinfbnd2 33671 nfaltop 34019 stoweidlem21 43237 stoweidlem47 43263 nfdfat 44291 |
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