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Mirrors > Home > NFE Home > Th. List > ibir | GIF version |
Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 22-Jul-2004.) |
Ref | Expression |
---|---|
ibir.1 | ⊢ (φ → (ψ ↔ φ)) |
Ref | Expression |
---|---|
ibir | ⊢ (φ → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ibir.1 | . . 3 ⊢ (φ → (ψ ↔ φ)) | |
2 | 1 | bicomd 192 | . 2 ⊢ (φ → (φ ↔ ψ)) |
3 | 2 | ibi 232 | 1 ⊢ (φ → ψ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: elpr2 3752 opkelimagekg 4271 ffdm 5234 ov 5595 enprmaplem6 6081 |
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