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Theorem 19.31 1876
Description: Theorem 19.31 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.31.1 xψ
Assertion
Ref Expression
19.31 (x(φ ψ) ↔ (xφ ψ))

Proof of Theorem 19.31
StepHypRef Expression
1 19.31.1 . . 3 xψ
2119.32 1875 . 2 (x(ψ φ) ↔ (ψ xφ))
3 orcom 376 . . 3 ((φ ψ) ↔ (ψ φ))
43albii 1566 . 2 (x(φ ψ) ↔ x(ψ φ))
5 orcom 376 . 2 ((xφ ψ) ↔ (ψ xφ))
62, 4, 53bitr4i 268 1 (x(φ ψ) ↔ (xφ ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wo 357  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-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-or 359  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  2eu3  2286
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