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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 828 | . 2 ⊢ (𝜓 → (𝜑 ↔ 𝜒)) |
3 | 2 | bicomd 129 | 1 ⊢ (𝜓 → (𝜒 ↔ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: rbaibr 831 pm5.44 834 exmoeu2 1948 ssnelpss 3289 r19.9rmv 3313 dfopg 3547 brinxp 4408 elioo5 8802 |
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