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Theorem r19.23v 2419
 Description: Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.)
Assertion
Ref Expression
r19.23v (x A (φψ) ↔ (x A φψ))
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x)   A(x)

Proof of Theorem r19.23v
StepHypRef Expression
1 nfv 1418 . 2 xψ
21r19.23 2418 1 (x A (φψ) ↔ (x A φψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀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-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:  uniiunlem  3022  dfiin2g  3681  iunss  3689  ralxfr2d  4162  rexxfr2d  4163  ssrel2  4373  reliun  4401  funimaexglem  4925  funimass4  5167  ralrnmpt2  5557
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