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Theorem r19.23 2418
Description: Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 22-Oct-2010.) (Proof shortened by Mario Carneiro, 8-Oct-2016.)
Hypothesis
Ref Expression
r19.23.1 xψ
Assertion
Ref Expression
r19.23 (x A (φψ) ↔ (x A φψ))

Proof of Theorem r19.23
StepHypRef Expression
1 r19.23.1 . 2 xψ
2 r19.23t 2417 . 2 (Ⅎxψ → (x A (φψ) ↔ (x A φψ)))
31, 2ax-mp 7 1 (x A (φψ) ↔ (x A φψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wnf 1346  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:  r19.23v  2419  rexlimi  2420  rexlimd  2424
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