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Theorem 19.27 1869
Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.27.1 xψ
Assertion
Ref Expression
19.27 (x(φ ψ) ↔ (xφ ψ))

Proof of Theorem 19.27
StepHypRef Expression
1 19.26 1593 . 2 (x(φ ψ) ↔ (xφ xψ))
2 19.27.1 . . . 4 xψ
3219.3 1785 . . 3 (xψψ)
43anbi2i 675 . 2 ((xφ xψ) ↔ (xφ ψ))
51, 4bitri 240 1 (x(φ ψ) ↔ (xφ ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358  wal 1540  wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
This theorem is referenced by:  aaan  1884  19.27v  1894
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