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Theorem exbi 1492
 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 111 . . . 4 ((φψ) → (φψ))
21alimi 1341 . . 3 (x(φψ) → x(φψ))
3 exim 1487 . . 3 (x(φψ) → (xφxψ))
42, 3syl 14 . 2 (x(φψ) → (xφxψ))
5 bi2 121 . . . 4 ((φψ) → (ψφ))
65alimi 1341 . . 3 (x(φψ) → x(ψφ))
7 exim 1487 . . 3 (x(ψφ) → (xψxφ))
86, 7syl 14 . 2 (x(φψ) → (xψxφ))
94, 8impbid 120 1 (x(φψ) → (xφxψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240  ∃wex 1378 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  exbii  1493  exbidh  1502  exintrbi  1521  19.19  1553  rexrnmpt  5253
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