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Theorem exbi 1581
Description: Theorem 19.18 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
exbi (x(φψ) → (xφxψ))

Proof of Theorem exbi
StepHypRef Expression
1 bi1 178 . . . 4 ((φψ) → (φψ))
21alimi 1559 . . 3 (x(φψ) → x(φψ))
3 exim 1575 . . 3 (x(φψ) → (xφxψ))
42, 3syl 15 . 2 (x(φψ) → (xφxψ))
5 bi2 189 . . . 4 ((φψ) → (ψφ))
65alimi 1559 . . 3 (x(φψ) → x(ψφ))
7 exim 1575 . . 3 (x(ψφ) → (xψxφ))
86, 7syl 15 . 2 (x(φψ) → (xψxφ))
94, 8impbid 183 1 (x(φψ) → (xφxψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  exbii  1582  exbidh  1591  exintrbi  1613  19.19  1862
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