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Mirrors > Home > MPE Home > Th. List > nfsuc | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for successor. (Contributed by NM, 15-Sep-2003.) |
Ref | Expression |
---|---|
nfsuc.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfsuc | ⊢ Ⅎ𝑥 suc 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-suc 6196 | . 2 ⊢ suc 𝐴 = (𝐴 ∪ {𝐴}) | |
2 | nfsuc.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfsn 4642 | . . 3 ⊢ Ⅎ𝑥{𝐴} |
4 | 2, 3 | nfun 4140 | . 2 ⊢ Ⅎ𝑥(𝐴 ∪ {𝐴}) |
5 | 1, 4 | nfcxfr 2975 | 1 ⊢ Ⅎ𝑥 suc 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2961 ∪ cun 3933 {csn 4566 suc csuc 6192 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-un 3940 df-sn 4567 df-pr 4569 df-suc 6196 |
This theorem is referenced by: rankidb 9228 dfon2lem3 33030 |
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