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Theorem sbceq1dd 3052
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
sbceq1d.1 (φA = B)
sbceq1dd.2 (φ → [̣A / xφ)
Assertion
Ref Expression
sbceq1dd (φ → [̣B / xφ)

Proof of Theorem sbceq1dd
StepHypRef Expression
1 sbceq1dd.2 . 2 (φ → [̣A / xφ)
2 sbceq1d.1 . . 3 (φA = B)
32sbceq1d 3051 . 2 (φ → ([̣A / xφ ↔ [̣B / xφ))
41, 3mpbid 201 1 (φ → [̣B / xφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1642  wsbc 3046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-cleq 2346  df-clel 2349  df-sbc 3047
This theorem is referenced by: (None)
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