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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 35940 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | nfaltop.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfsn 4712 | . . 3 ⊢ Ⅎ𝑥{𝐴} |
4 | nfaltop.2 | . . . . 5 ⊢ Ⅎ𝑥𝐵 | |
5 | 4 | nfsn 4712 | . . . 4 ⊢ Ⅎ𝑥{𝐵} |
6 | 2, 5 | nfpr 4697 | . . 3 ⊢ Ⅎ𝑥{𝐴, {𝐵}} |
7 | 3, 6 | nfpr 4697 | . 2 ⊢ Ⅎ𝑥{{𝐴}, {𝐴, {𝐵}}} |
8 | 1, 7 | nfcxfr 2901 | 1 ⊢ Ⅎ𝑥⟪𝐴, 𝐵⟫ |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2888 {csn 4631 {cpr 4633 ⟪caltop 35938 |
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 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-ex 1777 df-nf 1781 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-v 3480 df-un 3968 df-sn 4632 df-pr 4634 df-altop 35940 |
This theorem is referenced by: sbcaltop 35963 |
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