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Theorem rexlimiva 2406
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 2405 1 (x A φψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1374  wrex 2285
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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409  ax-i5r 1410
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-ral 2289  df-rex 2290
This theorem is referenced by:  unon  4186  dmaddpqlem  6236  nqpi  6237  nq0nn  6297  recexprlemm  6458  bj-nn0suc  7182  bj-nn0sucALT  7196
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