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Mirrors > Home > MPE Home > Th. List > hbimOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of hbim 2127 as of 6-Oct-2021. (Contributed by NM, 24-Jan-1993.) (Proof shortened by Mel L. O'Cat, 3-Mar-2008.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
hbimOLD.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
hbimOLD.2 | ⊢ (𝜓 → ∀𝑥𝜓) |
Ref | Expression |
---|---|
hbimOLD | ⊢ ((𝜑 → 𝜓) → ∀𝑥(𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbimOLD.1 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | hbimOLD.2 | . . 3 ⊢ (𝜓 → ∀𝑥𝜓) | |
3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
4 | 1, 3 | hbim1OLD 2227 | 1 ⊢ ((𝜑 → 𝜓) → ∀𝑥(𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nfOLD 1721 |
This theorem is referenced by: (None) |
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