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Mirrors > Home > NFE Home > Th. List > baib | GIF version |
Description: Move conjunction outside of biconditional. (Contributed by NM, 13-May-1999.) |
Ref | Expression |
---|---|
baib.1 | ⊢ (φ ↔ (ψ ∧ χ)) |
Ref | Expression |
---|---|
baib | ⊢ (ψ → (φ ↔ χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ibar 490 | . 2 ⊢ (ψ → (χ ↔ (ψ ∧ χ))) | |
2 | baib.1 | . 2 ⊢ (φ ↔ (ψ ∧ χ)) | |
3 | 1, 2 | syl6rbbr 255 | 1 ⊢ (ψ → (φ ↔ χ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358 |
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 df-an 360 |
This theorem is referenced by: baibr 872 rbaib 873 ceqsrexbv 2973 elrab3 2995 dfpss3 3355 rabsn 3790 elrint2 3968 fnres 5199 fvmpti 5699 |
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