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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 6165 | . 2 ⊢ suc 𝐴 = (𝐴 ∪ {𝐴}) | |
2 | nfsuc.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfsn 4603 | . . 3 ⊢ Ⅎ𝑥{𝐴} |
4 | 2, 3 | nfun 4092 | . 2 ⊢ Ⅎ𝑥(𝐴 ∪ {𝐴}) |
5 | 1, 4 | nfcxfr 2953 | 1 ⊢ Ⅎ𝑥 suc 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2936 ∪ cun 3879 {csn 4525 suc csuc 6161 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-v 3443 df-un 3886 df-sn 4526 df-pr 4528 df-suc 6165 |
This theorem is referenced by: rankidb 9213 dfon2lem3 33143 |
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