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Theorem 19.23 1801
 Description: Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.23.1 xψ
Assertion
Ref Expression
19.23 (x(φψ) ↔ (xφψ))

Proof of Theorem 19.23
StepHypRef Expression
1 19.23.1 . 2 xψ
2 19.23t 1800 . 2 (Ⅎxψ → (x(φψ) ↔ (xφψ)))
31, 2ax-mp 8 1 (x(φψ) ↔ (xφψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541  Ⅎwnf 1544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  19.23h  1802  exlimi  1803  exlimd  1806  nf2  1866  19.23v  1891  pm11.53  1893  ax10-16  2190  r19.3rz  3641  ralidm  3653
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