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Theorem r19.26-2 2436
Description: Theorem 19.26 of [Margaris] p. 90 with 2 restricted quantifiers. (Contributed by NM, 10-Aug-2004.)
Assertion
Ref Expression
r19.26-2 (x A y B (φ ψ) ↔ (x A y B φ x A y B ψ))

Proof of Theorem r19.26-2
StepHypRef Expression
1 r19.26 2435 . . 3 (y B (φ ψ) ↔ (y B φ y B ψ))
21ralbii 2324 . 2 (x A y B (φ ψ) ↔ x A (y B φ y B ψ))
3 r19.26 2435 . 2 (x A (y B φ y B ψ) ↔ (x A y B φ x A y B ψ))
42, 3bitri 173 1 (x A y B (φ ψ) ↔ (x A y B φ x A y B ψ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wral 2300
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-4 1397  ax-17 1416
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-ral 2305
This theorem is referenced by:  fununi  4908
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