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Mirrors > Home > MPE Home > Th. List > 19.35i | Structured version Visualization version GIF version |
Description: Inference associated with 19.35 1954. (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 1954 | . 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓)) | |
3 | 1, 2 | mpbi 220 | 1 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1630 ∃wex 1853 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 |
This theorem depends on definitions: df-bi 197 df-ex 1854 |
This theorem is referenced by: 19.2 2058 spimeh 2080 ax6e 2395 spimed 2400 equvini 2483 equvel 2484 euex 2631 axrep4 4927 zfcndrep 9648 bj-ax6elem2 32980 bj-spimedv 33047 bj-axrep4 33119 wl-exeq 33652 spd 42953 |
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