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Mirrors > Home > ILE Home > Th. List > Mathboxes > bd0 | GIF version |
Description: A formula equivalent to a bounded one is bounded. See also bd0r 9945. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bd0.min | ⊢ BOUNDED 𝜑 |
bd0.maj | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
bd0 | ⊢ BOUNDED 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bd0.min | . 2 ⊢ BOUNDED 𝜑 | |
2 | bd0.maj | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
3 | 2 | ax-bd0 9933 | . 2 ⊢ (BOUNDED 𝜑 → BOUNDED 𝜓) |
4 | 1, 3 | ax-mp 7 | 1 ⊢ BOUNDED 𝜓 |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 BOUNDED wbd 9932 |
This theorem was proved from axioms: ax-mp 7 ax-bd0 9933 |
This theorem is referenced by: bd0r 9945 bdth 9951 bdnth 9954 bdnthALT 9955 bdph 9970 bdsbc 9978 bdsnss 9993 bdcint 9997 bdeqsuc 10001 bdcriota 10003 bj-axun2 10035 |
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