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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 2026 when sufficient. (Contributed by Mel L. O'Cat, 31-Mar-2008.) |
Ref | Expression |
---|---|
19.2g | ⊢ (∀𝑥𝜑 → ∃𝑦𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a 2166 | . 2 ⊢ (𝜑 → ∃𝑦𝜑) | |
2 | 1 | sps 2169 | 1 ⊢ (∀𝑥𝜑 → ∃𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1599 ∃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 2055 ax-12 2163 |
This theorem depends on definitions: df-bi 199 df-ex 1824 |
This theorem is referenced by: (None) |
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