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Mirrors > Home > MPE Home > Th. List > mpbiri | Structured version Visualization version GIF version |
Description: An inference from a nested biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 25-Oct-2012.) |
Ref | Expression |
---|---|
mpbiri.min | ⊢ 𝜒 |
mpbiri.maj | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
mpbiri | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpbiri.min | . . 3 ⊢ 𝜒 | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → 𝜒) |
3 | mpbiri.maj | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
4 | 2, 3 | mpbird 256 | 1 ⊢ (𝜑 → 𝜓) |
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