Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > df-altop | Structured version Visualization version GIF version |
Description: An alternative definition of ordered pairs. This definition removes a hypothesis from its defining theorem (see altopth 34008), making it more convenient in some circumstances. (Contributed by Scott Fenton, 22-Mar-2012.) |
Ref | Expression |
---|---|
df-altop | ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | caltop 33995 | . 2 class ⟪𝐴, 𝐵⟫ |
4 | 1 | csn 4541 | . . 3 class {𝐴} |
5 | 2 | csn 4541 | . . . 4 class {𝐵} |
6 | 1, 5 | cpr 4543 | . . 3 class {𝐴, {𝐵}} |
7 | 4, 6 | cpr 4543 | . 2 class {{𝐴}, {𝐴, {𝐵}}} |
8 | 3, 7 | wceq 1543 | 1 wff ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} |
Colors of variables: wff setvar class |
This definition is referenced by: altopex 33999 altopthsn 34000 altxpsspw 34016 rankaltopb 34018 nfaltop 34019 |
Copyright terms: Public domain | W3C validator |