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Theorem sbsbc 3050

Description: Show that df-sb 1649 and df-sbc 3047 are equivalent when the class term A in df-sbc 3047 is a setvar variable. This theorem lets us reuse theorems based on df-sb 1649 for proofs involving df-sbc 3047. (Contributed by NM, 31-Dec-2016.) (Proof modification is discouraged.)

**Assertion**
Ref	Expression
sbsbc	⊢ ([y / x]φ ↔ [̣y / x]̣φ)

**Proof of Theorem sbsbc**
Step	Hyp	Ref	Expression
1		eqid 2353	. 2 ⊢ y = y
2		dfsbcq2 3049	. 2 ⊢ (y = y → ([y / x]φ ↔ [̣y / x]̣φ))
3	1, 2	ax-mp 8	1 ⊢ ([y / x]φ ↔ [̣y / x]̣φ)

Colors of variables: wff setvar class

Syntax hints: ↔ wb 176 [wsb 1648 [̣wsbc 3046

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-clab 2340 df-cleq 2346 df-clel 2349 df-sbc 3047

This theorem is referenced by: spsbc 3058 sbcid 3062 sbcco 3068 sbcco2 3069 sbcie2g 3079 eqsbc3 3085 sbcralt 3118 csbid 3143 sbnfc2 3196 csbabg 3197 cbvralcsf 3198 cbvreucsf 3200 cbvrabcsf 3201

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