Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > nfaltop | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for alternate ordered pairs. (Contributed by Scott Fenton, 25-Sep-2015.) |
Ref | Expression |
---|---|
nfaltop.1 | ⊢ Ⅎ𝑥𝐴 |
nfaltop.2 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfaltop | ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-altop 32065 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | nfaltop.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfsn 4242 | . . 3 ⊢ Ⅎ𝑥{𝐴} |
4 | nfaltop.2 | . . . . 5 ⊢ Ⅎ𝑥𝐵 | |
5 | 4 | nfsn 4242 | . . . 4 ⊢ Ⅎ𝑥{𝐵} |
6 | 2, 5 | nfpr 4232 | . . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}} |
7 | 3, 6 | nfpr 4232 | . 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}} |
8 | 1, 7 | nfcxfr 2762 | 1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫ |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2751 {csn 4177 {cpr 4179 ⟪caltop 32063 |
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-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-sn 4178 df-pr 4180 df-altop 32065 |
This theorem is referenced by: sbcaltop 32088 |
Copyright terms: Public domain | W3C validator |