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| Mirrors > Home > MPE Home > Th. List > 19.37iv | Structured version Visualization version GIF version | ||
| Description: Inference associated with 19.37v 1991. (Contributed by NM, 5-Aug-1993.) Remove dependency on ax-6 1967. (Revised by Rohan Ridenour, 15-Apr-2022.) | 
| Ref | Expression | 
|---|---|
| 19.37iv.1 | ⊢ ∃𝑥(𝜑 → 𝜓) | 
| Ref | Expression | 
|---|---|
| 19.37iv | ⊢ (𝜑 → ∃𝑥𝜓) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | 19.37iv.1 | . 2 ⊢ ∃𝑥(𝜑 → 𝜓) | |
| 2 | 19.37imv 1947 | . 2 ⊢ (∃𝑥(𝜑 → 𝜓) → (𝜑 → ∃𝑥𝜓)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → ∃𝑥𝜓) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∃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 | 
| This theorem depends on definitions: df-bi 207 df-ex 1780 | 
| This theorem is referenced by: bnd 9932 zfcndinf 10658 bnj1093 34994 bnj1186 35021 relopabVD 44921 elpglem2 49231 | 
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