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Mirrors > Home > ILE Home > Th. List > baibr | GIF version |
Description: Move conjunction outside of biconditional. (Contributed by NM, 11-Jul-1994.) |
Ref | Expression |
---|---|
baib.1 | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) |
Ref | Expression |
---|---|
baibr | ⊢ (𝜓 → (𝜒 ↔ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | baib.1 | . . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒)) | |
2 | 1 | baib 872 | . 2 ⊢ (𝜓 → (𝜑 ↔ 𝜒)) |
3 | 2 | bicomd 140 | 1 ⊢ (𝜓 → (𝜒 ↔ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ↔ wb 104 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: rbaibr 875 pm5.44 878 exmoeu2 2008 r19.9rmv 3401 dfopg 3650 brinxp 4545 elioo5 9557 prmind2 11594 |
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