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Theorem r19.29d2r 2449
Description: Theorem 19.29 of [Margaris] p. 90 with two restricted quantifiers, deduction version (Contributed by Thierry Arnoux, 30-Jan-2017.)
Hypotheses
Ref Expression
r19.29d2r.1 (φx A y B ψ)
r19.29d2r.2 (φx A y B χ)
Assertion
Ref Expression
r19.29d2r (φx A y B (ψ χ))

Proof of Theorem r19.29d2r
StepHypRef Expression
1 r19.29d2r.1 . . 3 (φx A y B ψ)
2 r19.29d2r.2 . . 3 (φx A y B χ)
3 r19.29 2444 . . 3 ((x A y B ψ x A y B χ) → x A (y B ψ y B χ))
41, 2, 3syl2anc 391 . 2 (φx A (y B ψ y B χ))
5 r19.29 2444 . . 3 ((y B ψ y B χ) → y B (ψ χ))
65reximi 2410 . 2 (x A (y B ψ y B χ) → x A y B (ψ χ))
74, 6syl 14 1 (φx A y B (ψ χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wral 2300  wrex 2301
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-ial 1424
This theorem depends on definitions:  df-bi 110  df-ral 2305  df-rex 2306
This theorem is referenced by:  r19.29vva  2450
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