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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-1 5  ax-2 6  ax-3 7  ax-mp 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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