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Theorem rmoeqd 2818
Description: Equality deduction for restricted uniqueness quantifier. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
raleqd.1 (A = B → (φψ))
Assertion
Ref Expression
rmoeqd (A = B → (∃*x A φ∃*x B ψ))
Distinct variable groups:   x,A   x,B
Allowed substitution hints:   φ(x)   ψ(x)

Proof of Theorem rmoeqd
StepHypRef Expression
1 rmoeq1 2810 . 2 (A = B → (∃*x A φ∃*x B φ))
2 raleqd.1 . . 3 (A = B → (φψ))
32rmobidv 2800 . 2 (A = B → (∃*x B φ∃*x B ψ))
41, 3bitrd 244 1 (A = B → (∃*x A φ∃*x B ψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   = wceq 1642  ∃*wrmo 2617
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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rmo 2622
This theorem is referenced by: (None)
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