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Mirrors > Home > MPE Home > Th. List > Mathboxes > 19.8ad | Structured version Visualization version GIF version |
Description: If a wff is true, it is true for at least one instance. Deduction form of 19.8a 2165. (Contributed by DAW, 13-Feb-2017.) |
Ref | Expression |
---|---|
19.8ad.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.8ad | ⊢ (𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8ad.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | 19.8a 2165 | . 2 ⊢ (𝜓 → ∃𝑥𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1823 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2054 ax-12 2162 |
This theorem depends on definitions: df-bi 199 df-ex 1824 |
This theorem is referenced by: (None) |
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