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Metamath Proof Explorer

Theorem suceqd

Description: Deduction associated with suceq . (Contributed by Rohan Ridenour, 8-Aug-2023)

		Ref	Expression
	Hypothesis	suceqd.1	$⊢ φ \to A = B$
	Assertion	suceqd	$⊢ φ \to suc A = suc B$

Step	Hyp	Ref	Expression
1		suceqd.1	$⊢ φ \to A = B$
2	1	sneqd	$⊢ φ \to \{A\} = \{B\}$
3	1 2	uneq12d	$⊢ φ \to A \cup \{A\} = B \cup \{B\}$
4		df-suc	$⊢ suc A = A \cup \{A\}$
5		df-suc	$⊢ suc B = B \cup \{B\}$
6	3 4 5	3eqtr4g	$⊢ φ \to suc A = suc B$