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Metamath Proof Explorer

Theorem pm5.74d

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 21-Mar-1996)

Ref Expression
Hypothesis pm5.74d.1 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ↔ 𝜃 ) ) )
Assertion pm5.74d ( 𝜑 → ( ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) )

Proof

Step Hyp Ref Expression
1 pm5.74d.1 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ↔ 𝜃 ) ) )
2 pm5.74 ⊢ ( ( 𝜓 → ( 𝜒 ↔ 𝜃 ) ) ↔ ( ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) )
3 1 2 sylib ⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) )