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Mirrors > Home > NFE Home > Th. List > a1bi | GIF version |
Description: Inference rule introducing a theorem as an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 11-Nov-2012.) |
Ref | Expression |
---|---|
a1bi.1 | ⊢ φ |
Ref | Expression |
---|---|
a1bi | ⊢ (ψ ↔ (φ → ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a1bi.1 | . 2 ⊢ φ | |
2 | biimt 325 | . 2 ⊢ (φ → (ψ ↔ (φ → ψ))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (ψ ↔ (φ → ψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: mt2bi 328 pm4.83 895 truimfal 1345 equsalhw 1838 equveli 1988 sbequ8 2079 ralv 2873 ssopr 4847 |
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