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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 33414 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | nfaltop.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfsn 4636 | . . 3 ⊢ Ⅎ𝑥{𝐴} |
4 | nfaltop.2 | . . . . 5 ⊢ Ⅎ𝑥𝐵 | |
5 | 4 | nfsn 4636 | . . . 4 ⊢ Ⅎ𝑥{𝐵} |
6 | 2, 5 | nfpr 4621 | . . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}} |
7 | 3, 6 | nfpr 4621 | . 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}} |
8 | 1, 7 | nfcxfr 2975 | 1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫ |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2961 {csn 4560 {cpr 4562 ⟪caltop 33412 |
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 4561 df-pr 4563 df-altop 33414 |
This theorem is referenced by: sbcaltop 33437 |
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