Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 19.23v | GIF version |
Description: Special case of Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jun-1998.) |
Ref | Expression |
---|---|
19.23v | ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1506 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
2 | 1 | 19.23h 1478 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 ∀wal 1333 ∃wex 1472 |
This theorem was proved from axioms: ax-mp 5 ax-gen 1429 ax-ie2 1474 ax-17 1506 |
This theorem is referenced by: 19.23vv 1864 2eu4 2099 gencbval 2760 euind 2899 reuind 2917 unissb 3802 disjnim 3956 dftr2 4064 ssrelrel 4685 cotr 4966 dffun2 5179 fununi 5237 dff13 5715 acexmidlem2 5818 |
Copyright terms: Public domain | W3C validator |