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Mirrors > Home > MPE Home > Th. List > exlimdhOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of exlimdh 2134 as of 6-Oct-2021. (Contributed by NM, 28-Jan-1997.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
exlimdhOLD.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
exlimdhOLD.2 | ⊢ (𝜒 → ∀𝑥𝜒) |
exlimdhOLD.3 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
exlimdhOLD | ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimdhOLD.1 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | nfiOLD 1725 | . 2 ⊢ Ⅎ𝑥𝜑 |
3 | exlimdhOLD.2 | . . 3 ⊢ (𝜒 → ∀𝑥𝜒) | |
4 | 3 | nfiOLD 1725 | . 2 ⊢ Ⅎ𝑥𝜒 |
5 | exlimdhOLD.3 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
6 | 2, 4, 5 | exlimdOLD 2211 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
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 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nfOLD 1712 |
This theorem is referenced by: (None) |
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