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Theorem 19.36-1 1560
 Description: Closed form of 19.36i 1559. One direction of Theorem 19.36 of [Margaris] p. 90. The converse holds in classical logic, but does not hold (for all propositions) in intuitionistic logic. (Contributed by Jim Kingdon, 20-Jun-2018.)
Hypothesis
Ref Expression
19.36-1.1 xψ
Assertion
Ref Expression
19.36-1 (x(φψ) → (xφψ))

Proof of Theorem 19.36-1
StepHypRef Expression
1 19.35-1 1512 . 2 (x(φψ) → (xφxψ))
2 19.36-1.1 . . 3 xψ
3219.9 1532 . 2 (xψψ)
41, 3syl6ib 150 1 (x(φψ) → (xφψ))
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240  Ⅎwnf 1346  ∃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  df-nf 1347 This theorem is referenced by:  vtocl2  2603  vtocl3  2604  spcimgft  2623
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