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Metamath Proof Explorer
Description: Distribution of implication over biconditional (reverse inference form).
(Contributed by NM, 1-Aug-1994)
|
|
Ref |
Expression |
|
Hypothesis |
pm5.74ri.1 |
⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → 𝜒 ) ) |
|
Assertion |
pm5.74ri |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm5.74ri.1 |
⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → 𝜒 ) ) |
| 2 |
|
pm5.74 |
⊢ ( ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) ↔ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → 𝜒 ) ) ) |
| 3 |
1 2
|
mpbir |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |