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Mirrors > Home > MPE Home > Th. List > 19.35i | Structured version Visualization version GIF version |
Description: Inference associated with 19.35 1794. (Contributed by NM, 21-Jun-1993.) |
Ref | Expression |
---|---|
19.35i.1 | ⊢ ∃𝑥(𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.35i | ⊢ (∀𝑥𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.35i.1 | . 2 ⊢ ∃𝑥(𝜑 → 𝜓) | |
2 | 19.35 1794 | . 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓)) | |
3 | 1, 2 | mpbi 219 | 1 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: 19.2 1879 spimeh 1912 cbv3hvOLD 2161 cbv3hvOLDOLD 2162 ax6e 2238 spimed 2243 equvini 2334 equvel 2335 euex 2482 axrep4 4703 zfcndrep 9315 bj-ax6elem2 31841 bj-spimedv 31906 bj-axrep4 31979 wl-exeq 32500 spd 42223 |
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