Theorem suceqd

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

	Ref	Expression
Hypothesis	suceqd.1	|- ( ph -> A = B )
Assertion	suceqd	|- ( ph -> suc A = suc B )

Proof

Step	Hyp	Ref	Expression
1		suceqd.1	|- ( ph -> A = B )
2	1	sneqd	|- ( ph -> { A } = { B } )
3	1 2	uneq12d	|- ( ph -> ( A u. { A } ) = ( B u. { B } ) )
4		df-suc	|- suc A = ( A u. { A } )
5		df-suc	|- suc B = ( B u. { B } )
6	3 4 5	3eqtr4g	|- ( ph -> suc A = suc B )