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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-exlimmpbir | Structured version Visualization version GIF version |
Description: Lemma for theorems of the vtoclg 3470 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-exlimmpbir.nf | ⊢ Ⅎ𝑥𝜑 |
bj-exlimmpbir.maj | ⊢ (𝜒 → (𝜑 ↔ 𝜓)) |
bj-exlimmpbir.min | ⊢ 𝜓 |
Ref | Expression |
---|---|
bj-exlimmpbir | ⊢ (∃𝑥𝜒 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-exlimmpbir.nf | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | bj-exlimmpbir.min | . . 3 ⊢ 𝜓 | |
3 | bj-exlimmpbir.maj | . . 3 ⊢ (𝜒 → (𝜑 ↔ 𝜓)) | |
4 | 2, 3 | mpbiri 261 | . 2 ⊢ (𝜒 → 𝜑) |
5 | 1, 4 | exlimi 2219 | 1 ⊢ (∃𝑥𝜒 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∃wex 1786 Ⅎwnf 1790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-12 2179 |
This theorem depends on definitions: df-bi 210 df-ex 1787 df-nf 1791 |
This theorem is referenced by: (None) |
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