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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 35959 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
| 2 | nfaltop.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
| 3 | 2 | nfsn 4707 | . . 3 ⊢ Ⅎ𝑥{𝐴} | 
| 4 | nfaltop.2 | . . . . 5 ⊢ Ⅎ𝑥𝐵 | |
| 5 | 4 | nfsn 4707 | . . . 4 ⊢ Ⅎ𝑥{𝐵} | 
| 6 | 2, 5 | nfpr 4692 | . . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}} | 
| 7 | 3, 6 | nfpr 4692 | . 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}} | 
| 8 | 1, 7 | nfcxfr 2903 | 1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫ | 
| Colors of variables: wff setvar class | 
| Syntax hints: Ⅎwnfc 2890 {csn 4626 {cpr 4628 ⟪caltop 35957 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-nf 1784 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-v 3482 df-un 3956 df-sn 4627 df-pr 4629 df-altop 35959 | 
| This theorem is referenced by: sbcaltop 35982 | 
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