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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 35235 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | nfaltop.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfsn 4711 | . . 3 ⊢ Ⅎ𝑥{𝐴} |
4 | nfaltop.2 | . . . . 5 ⊢ Ⅎ𝑥𝐵 | |
5 | 4 | nfsn 4711 | . . . 4 ⊢ Ⅎ𝑥{𝐵} |
6 | 2, 5 | nfpr 4694 | . . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}} |
7 | 3, 6 | nfpr 4694 | . 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}} |
8 | 1, 7 | nfcxfr 2900 | 1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫ |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2882 {csn 4628 {cpr 4630 ⟪caltop 35233 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1543 df-ex 1781 df-nf 1785 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-v 3475 df-un 3953 df-sn 4629 df-pr 4631 df-altop 35235 |
This theorem is referenced by: sbcaltop 35258 |
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