This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem aecoms-o

Description: A commutation rule for identical variable specifiers. Version of aecoms using ax-c11 . (Contributed by NM, 10-May-1993) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	alequcoms-o.1	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → 𝜑 )
	Assertion	aecoms-o	⊢ ( ∀ 𝑦 𝑦 = 𝑥 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		alequcoms-o.1	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → 𝜑 )
2		aecom-o	⊢ ( ∀ 𝑦 𝑦 = 𝑥 → ∀ 𝑥 𝑥 = 𝑦 )
3	2 1	syl	⊢ ( ∀ 𝑦 𝑦 = 𝑥 → 𝜑 )