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

Metamath Proof Explorer

Theorem s1eqd

Description: Equality theorem for a singleton word. (Contributed by Mario Carneiro, 26-Feb-2016)

		Ref	Expression
	Hypothesis	s1eqd.1	$⊢ φ \to A = B$
	Assertion	s1eqd	$⊢ φ \to ⟨“ A ”⟩ = ⟨“ B ”⟩$

Step	Hyp	Ref	Expression
1		s1eqd.1	$⊢ φ \to A = B$
2		s1eq	$⊢ A = B \to ⟨“ A ”⟩ = ⟨“ B ”⟩$
3	1 2	syl	$⊢ φ \to ⟨“ A ”⟩ = ⟨“ B ”⟩$