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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 4138 | . 2 ⊢ {𝐴} = {𝐴, 𝐴} | |
2 | nfsn.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | 2, 2 | nfpr 4179 | . 2 ⊢ Ⅎ𝑥{𝐴, 𝐴} |
4 | 1, 3 | nfcxfr 2749 | 1 ⊢ Ⅎ𝑥{𝐴} |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2738 {csn 4125 {cpr 4127 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-un 3545 df-sn 4126 df-pr 4128 |
This theorem is referenced by: nfop 4356 iunopeqop 4906 nfpred 5602 nfsuc 5713 sniota 5795 dfmpt2 7154 bnj958 30264 bnj1000 30265 bnj1446 30367 bnj1447 30368 bnj1448 30369 bnj1466 30375 bnj1467 30376 nfaltop 31257 stoweidlem21 38914 stoweidlem47 38940 nfdfat 39859 |
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