Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsbcALT | GIF version |
Description: Alternate proof of bdsbc 13045. (Contributed by BJ, 16-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bdcsbc.1 | ⊢ BOUNDED 𝜑 |
Ref | Expression |
---|---|
bdsbcALT | ⊢ BOUNDED [𝑦 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcsbc.1 | . . 3 ⊢ BOUNDED 𝜑 | |
2 | 1 | bdab 13025 | . 2 ⊢ BOUNDED 𝑦 ∈ {𝑥 ∣ 𝜑} |
3 | df-sbc 2905 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
4 | 2, 3 | bd0r 13012 | 1 ⊢ BOUNDED [𝑦 / 𝑥]𝜑 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 {cab 2123 [wsbc 2904 BOUNDED wbd 12999 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-bd0 13000 ax-bdsb 13009 |
This theorem depends on definitions: df-bi 116 df-clab 2124 df-sbc 2905 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |