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Mirrors > Home > MPE Home > Th. List > 19.8v | Structured version Visualization version GIF version |
Description: Version of 19.8a 2039 with a dv condition, requiring fewer axioms. (Contributed by BJ, 12-Mar-2020.) |
Ref | Expression |
---|---|
19.8v | ⊢ (𝜑 → ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1827 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | 19.8w 1881 | 1 ⊢ (𝜑 → ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: 19.9v 1883 |
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