Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > rbaibd | Structured version Visualization version GIF version |
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.) |
Ref | Expression |
---|---|
baibd.1 | ⊢ (𝜑 → (𝜓 ↔ (𝜒 ∧ 𝜃))) |
Ref | Expression |
---|---|
rbaibd | ⊢ ((𝜑 ∧ 𝜃) → (𝜓 ↔ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | baibd.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ (𝜒 ∧ 𝜃))) | |
2 | 1 | biancomd 464 | . 2 ⊢ (𝜑 → (𝜓 ↔ (𝜃 ∧ 𝜒))) |
3 | 2 | baibd 540 | 1 ⊢ ((𝜑 ∧ 𝜃) → (𝜓 ↔ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ wa 396 |
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 206 df-an 397 |
This theorem is referenced by: qsqueeze 12934 o1lo12 15245 incexc2 15548 gexdvds 19187 fsumvma 26359 qusker 31545 |
Copyright terms: Public domain | W3C validator |