![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > 19.23bi | Structured version Visualization version GIF version |
Description: Inference form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2254. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
19.23bi.1 | ⊢ (∃𝑥𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.23bi | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a 2223 | . 2 ⊢ (𝜑 → ∃𝑥𝜑) | |
2 | 19.23bi.1 | . 2 ⊢ (∃𝑥𝜑 → 𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1878 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-12 2220 |
This theorem depends on definitions: df-bi 199 df-ex 1879 |
This theorem is referenced by: nf5ri 2236 equs5eALT 2387 equs5e 2479 dfmo 2668 2mo 2731 copsexg 5178 axreg2 8774 hash1to3 13569 ustuqtop4 22425 f1omptsnlem 33728 mptsnunlem 33730 |
Copyright terms: Public domain | W3C validator |