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Theorem rexlimd2 2425
Description: Version of rexlimd 2424 with deduction version of second hypothesis. (Contributed by NM, 21-Jul-2013.) (Revised by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
rexlimd2.1 xφ
rexlimd2.2 (φ → Ⅎxχ)
rexlimd2.3 (φ → (x A → (ψχ)))
Assertion
Ref Expression
rexlimd2 (φ → (x A ψχ))

Proof of Theorem rexlimd2
StepHypRef Expression
1 rexlimd2.1 . . 3 xφ
2 rexlimd2.3 . . 3 (φ → (x A → (ψχ)))
31, 2ralrimi 2384 . 2 (φx A (ψχ))
4 rexlimd2.2 . . 3 (φ → Ⅎxχ)
5 r19.23t 2417 . . 3 (Ⅎxχ → (x A (ψχ) ↔ (x A ψχ)))
64, 5syl 14 . 2 (φ → (x A (ψχ) ↔ (x A ψχ)))
73, 6mpbid 135 1 (φ → (x A ψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wnf 1346   wcel 1390  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  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306
This theorem is referenced by: (None)
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