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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-spnfw | Structured version Visualization version GIF version |
Description: Theorem close to a closed form of spnfw 1989. (Contributed by BJ, 12-May-2019.) |
Ref | Expression |
---|---|
bj-spnfw | ⊢ ((∃𝑥𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.2 1986 | . 2 ⊢ (∀𝑥𝜑 → ∃𝑥𝜑) | |
2 | 1 | imim1i 63 | 1 ⊢ ((∃𝑥𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 ∃wex 1786 |
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-6 1975 |
This theorem depends on definitions: df-bi 210 df-ex 1787 |
This theorem is referenced by: (None) |
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