Metamath Proof Explorer
Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994)
|
|
Ref |
Expression |
|
Hypotheses |
mpbidi.min |
⊢ ( 𝜃 → ( 𝜑 → 𝜓 ) ) |
|
|
mpbidi.maj |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
|
Assertion |
mpbidi |
⊢ ( 𝜃 → ( 𝜑 → 𝜒 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
mpbidi.min |
⊢ ( 𝜃 → ( 𝜑 → 𝜓 ) ) |
2 |
|
mpbidi.maj |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
3 |
2
|
biimpd |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
4 |
1 3
|
sylcom |
⊢ ( 𝜃 → ( 𝜑 → 𝜒 ) ) |