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Mirrors > Home > MPE Home > Th. List > 19.36iv | Structured version Visualization version GIF version |
Description: Inference associated with 19.36v 1996. Version of 19.36i 2229 with a disjoint variable condition. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.) Remove dependency on ax-6 1976. (Revised by Rohan Ridenour, 15-Apr-2022.) |
Ref | Expression |
---|---|
19.36iv.1 | ⊢ ∃𝑥(𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.36iv | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.36iv.1 | . 2 ⊢ ∃𝑥(𝜑 → 𝜓) | |
2 | 19.36imv 1953 | . 2 ⊢ (∃𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1541 ∃wex 1787 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 |
This theorem depends on definitions: df-bi 210 df-ex 1788 |
This theorem is referenced by: spimvALT 2390 zfcndext 10224 |
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