![]() |
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 2209. (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 2178 | . 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 1781 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-12 2175 |
This theorem depends on definitions: df-bi 210 df-ex 1782 |
This theorem is referenced by: nf5ri 2193 equs5eALT 2374 equs5e 2470 2mo 2710 copsexg 5347 axreg2 9041 hash1to3 13845 ustuqtop4 22850 f1omptsnlem 34753 mptsnunlem 34755 |
Copyright terms: Public domain | W3C validator |