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Theorem 19.37-1 1545
Description: One direction of Theorem 19.37 of [Margaris] p. 90. The converse holds in classical logic but not, in general, here. (Contributed by Jim Kingdon, 21-Jun-2018.)
Hypothesis
Ref Expression
19.37-1.1 xφ
Assertion
Ref Expression
19.37-1 (x(φψ) → (φxψ))

Proof of Theorem 19.37-1
StepHypRef Expression
1 19.37-1.1 . . 3 xφ
2119.3 1429 . 2 (xφφ)
3 19.35-1 1498 . 2 (x(φψ) → (xφxψ))
42, 3syl5bir 142 1 (x(φψ) → (φxψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1314  wnf 1328  wex 1361
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 1315  ax-gen 1317  ax-ie1 1362  ax-ie2 1363  ax-4 1382  ax-ial 1410
This theorem depends on definitions:  df-bi 110  df-nf 1329
This theorem is referenced by:  19.37aiv  1546  spcimegft  2606  eqvincg  2643
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