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Theorem rexlimiva 2422
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006.)
Hypothesis
Ref Expression
rexlimiva.1 ((x A φ) → ψ)
Assertion
Ref Expression
rexlimiva (x A φψ)
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x)   A(x)

Proof of Theorem rexlimiva
StepHypRef Expression
1 rexlimiva.1 . . 3 ((x A φ) → ψ)
21ex 108 . 2 (x A → (φψ))
32rexlimiv 2421 1 (x A φψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1390  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-17 1416  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:  unon  4202  ssfiexmid  6254  dmaddpqlem  6361  nqpi  6362  nq0nn  6424  recexprlemm  6594  bj-nn0suc  9348  bj-nn0sucALT  9362
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