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Theorem sbceq1dd 2764
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by NM, 30-Jun-2018.)
Hypotheses
Ref Expression
sbceq1d.1 (φA = B)
sbceq1dd.2 (φ[A / x]ψ)
Assertion
Ref Expression
sbceq1dd (φ[B / x]ψ)

Proof of Theorem sbceq1dd
StepHypRef Expression
1 sbceq1dd.2 . 2 (φ[A / x]ψ)
2 sbceq1d.1 . . 3 (φA = B)
32sbceq1d 2763 . 2 (φ → ([A / x]ψ[B / x]ψ))
41, 3mpbid 135 1 (φ[B / x]ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  [wsbc 2758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033  df-sbc 2759
This theorem is referenced by: (None)
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