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Metamath Proof Explorer

Theorem equcomiv

Description: Weaker form of equcomi with a disjoint variable condition on x , y . This is an intermediate step and equcomi is fully recovered later. (Contributed by BJ, 7-Dec-2020)

		Ref	Expression
	Assertion	equcomiv	⊢ ( 𝑥 = 𝑦 → 𝑦 = 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		equid	⊢ 𝑥 = 𝑥
2		ax7v2	⊢ ( 𝑥 = 𝑦 → ( 𝑥 = 𝑥 → 𝑦 = 𝑥 ) )
3	1 2	mpi	⊢ ( 𝑥 = 𝑦 → 𝑦 = 𝑥 )