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Metamath Proof Explorer

Theorem equsb3

Description: Substitution in an equality. (Contributed by Raph Levien and FL, 4-Dec-2005) Reduce axiom usage. (Revised by Wolf Lammen, 23-Jul-2023)

		Ref	Expression
	Assertion	equsb3	$⊢ [y/ x] x = z \leftrightarrow y = z$

Proof

Step	Hyp	Ref	Expression
1		equequ1	$⊢ x = w \to (x = z \leftrightarrow w = z)$
2		equequ1	$⊢ w = y \to (w = z \leftrightarrow y = z)$
3	1 2	sbievw2	$⊢ [y/ x] x = z \leftrightarrow y = z$