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Mirrors > Home > MPE Home > Th. List > Mathboxes > exinst | Structured version Visualization version GIF version |
Description: Existential Instantiation. Virtual deduction form of exlimexi 44436. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
exinst.1 | ⊢ (𝜓 → ∀𝑥𝜓) |
exinst.2 | ⊢ ( ∃𝑥𝜑 , 𝜑 ▶ 𝜓 ) |
Ref | Expression |
---|---|
exinst | ⊢ (∃𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exinst.1 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
2 | exinst.2 | . . 3 ⊢ ( ∃𝑥𝜑 , 𝜑 ▶ 𝜓 ) | |
3 | 2 | dfvd2i 44497 | . 2 ⊢ (∃𝑥𝜑 → (𝜑 → 𝜓)) |
4 | 1, 3 | exlimexi 44436 | 1 ⊢ (∃𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1535 ∃wex 1777 ( wvd2 44489 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-10 2136 ax-12 2173 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1778 df-nf 1782 df-vd2 44490 |
This theorem is referenced by: sb5ALTVD 44825 |
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