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Metamath Proof Explorer

Theorem sb2imi

Description: Distribute substitution over implication. Compare al2imi . (Contributed by Steven Nguyen, 13-Aug-2023)

		Ref	Expression
	Hypothesis	sb2imi.1	$⊢ φ \to (ψ \to χ)$
	Assertion	sb2imi	$⊢ [t/ x] φ \to ([t/ x] ψ \to [t/ x] χ)$

Step	Hyp	Ref	Expression
1		sb2imi.1	$⊢ φ \to (ψ \to χ)$
2	1	sbimi	$⊢ [t/ x] φ \to [t/ x] (ψ \to χ)$
3		sbi1	$⊢ [t/ x] (ψ \to χ) \to ([t/ x] ψ \to [t/ x] χ)$
4	2 3	syl	$⊢ [t/ x] φ \to ([t/ x] ψ \to [t/ x] χ)$