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Mirrors > Home > MPE Home > Th. List > 19.37iv | Structured version Visualization version GIF version |
Description: Inference associated with 19.37v 2040. (Contributed by NM, 5-Aug-1993.) Remove dependency on ax-6 2021. (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 1990 | . 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 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 |
This theorem depends on definitions: df-bi 199 df-ex 1824 |
This theorem is referenced by: bnd 9052 zfcndinf 9775 bnj1093 31647 bnj1186 31674 relopabVD 40070 elpglem2 43563 |
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