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| Mirrors > Home > MPE Home > Th. List > 19.2g | Structured version Visualization version GIF version | ||
| Description: Theorem 19.2 of [Margaris] p. 89, generalized to use two setvar variables. Use 19.2 1976 when sufficient. (Contributed by Mel L. O'Cat, 31-Mar-2008.) |
| Ref | Expression |
|---|---|
| 19.2g | ⊢ (∀𝑥𝜑 → ∃𝑦𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.8a 2181 | . 2 ⊢ (𝜑 → ∃𝑦𝜑) | |
| 2 | 1 | sps 2185 | 1 ⊢ (∀𝑥𝜑 → ∃𝑦𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∀wal 1538 ∃wex 1779 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-ex 1780 |
| This theorem is referenced by: (None) |
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