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Theorem 3eltr3g 2435
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr3g.1 (φA B)
3eltr3g.2 A = C
3eltr3g.3 B = D
Assertion
Ref Expression
3eltr3g (φC D)

Proof of Theorem 3eltr3g
StepHypRef Expression
1 3eltr3g.1 . 2 (φA B)
2 3eltr3g.2 . . 3 A = C
3 3eltr3g.3 . . 3 B = D
42, 3eleq12i 2418 . 2 (A BC D)
51, 4sylib 188 1 (φC D)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1642   wcel 1710
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
This theorem is referenced by: (None)
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