Theorem recseq

Description: Equality theorem for recs . (Contributed by Stefan O'Rear, 18-Jan-2015)

	Ref	Expression
Assertion	recseq	$$⊢F=G\to \mathrm{recs}\left(F\right)=\mathrm{recs}\left(G\right)$$

Proof

Step	Hyp	Ref	Expression
1		wrecseq3	$$⊢F=G\to \mathrm{wrecs}\left(\mathrm{E},\mathrm{On},F\right)=\mathrm{wrecs}\left(\mathrm{E},\mathrm{On},G\right)$$
2		df-recs	$$⊢\mathrm{recs}\left(F\right)=\mathrm{wrecs}\left(\mathrm{E},\mathrm{On},F\right)$$
3		df-recs	$$⊢\mathrm{recs}\left(G\right)=\mathrm{wrecs}\left(\mathrm{E},\mathrm{On},G\right)$$
4	1 2 3	3eqtr4g	$$⊢F=G\to \mathrm{recs}\left(F\right)=\mathrm{recs}\left(G\right)$$