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Mirrors > Home > MPE Home > Th. List > hbsbwOLD | Structured version Visualization version GIF version |
Description: Obsolete version of hbsbw 2174 as of 23-May-2024. (Contributed by NM, 12-Aug-1993.) (Revised by Gino Giotto, 10-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
hbsbwOLD.1 | ⊢ (𝜑 → ∀𝑧𝜑) |
Ref | Expression |
---|---|
hbsbwOLD | ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑧[𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbsbwOLD.1 | . . . 4 ⊢ (𝜑 → ∀𝑧𝜑) | |
2 | 1 | nf5i 2148 | . . 3 ⊢ Ⅎ𝑧𝜑 |
3 | 2 | nfsbv 2339 | . 2 ⊢ Ⅎ𝑧[𝑦 / 𝑥]𝜑 |
4 | 3 | nf5ri 2194 | 1 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑧[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1537 [wsb 2070 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1912 ax-6 1971 ax-7 2016 ax-10 2143 ax-11 2159 ax-12 2176 |
This theorem depends on definitions: df-bi 210 df-an 401 df-ex 1783 df-nf 1787 df-sb 2071 |
This theorem is referenced by: (None) |
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