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Mirrors > Home > MPE Home > Th. List > nfriOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nf5ri 2053 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfriOLD.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfriOLD | ⊢ (𝜑 → ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfriOLD.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | nfrOLD 2176 | . 2 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ℲwnfOLD 1700 |
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-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nfOLD 1712 |
This theorem is referenced by: alimdOLD 2179 alrimiOLD 2180 eximdOLD 2185 nexdOLD 2186 albidOLD 2187 exbidOLD 2188 19.3OLD 2190 nfim1OLD 2216 hbanOLD 2228 hb3anOLD 2229 |
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