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Mirrors > Home > MPE Home > Th. List > moimiOLD | Structured version Visualization version GIF version |
Description: Obsolete version of moimi 2621 as of 9-May-2023. The at-most-one quantifier reverses implication. (Contributed by NM, 15-Feb-2006.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
moimiOLD.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
moimiOLD | ⊢ (∃*𝑥𝜓 → ∃*𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | moim 2620 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑)) | |
2 | moimiOLD.1 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | mpg 1792 | 1 ⊢ (∃*𝑥𝜓 → ∃*𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃*wmo 2614 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 |
This theorem depends on definitions: df-bi 209 df-ex 1775 df-mo 2616 |
This theorem is referenced by: (None) |
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