Theorem ralabsod

Description: Deduction form of ralabso . (Contributed by Eric Schmidt, 19-Oct-2025)

	Ref	Expression
Hypothesis	ralabsod.1	$$⊢\phi \to \mathrm{Tr}M$$
Assertion	ralabsod	$$⊢\left(\phi \wedge A\in M\right)\to \left(\forall x\in A\psi \leftrightarrow \forall x\in M\left(x\in A\to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ralabsod.1	$$⊢\phi \to \mathrm{Tr}M$$
2		ralabso	$$⊢\left(\mathrm{Tr}M\wedge A\in M\right)\to \left(\forall x\in A\psi \leftrightarrow \forall x\in M\left(x\in A\to \psi \right)\right)$$
3	1 2	sylan	$$⊢\left(\phi \wedge A\in M\right)\to \left(\forall x\in A\psi \leftrightarrow \forall x\in M\left(x\in A\to \psi \right)\right)$$