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Theorem 19.35-1 1499
Description: Forward direction of Theorem 19.35 of [Margaris] p. 90. The converse holds for classical logic but not (for all propositions) in intuitionistic logic (Contributed by Mario Carneiro, 2-Feb-2015.)
Assertion
Ref Expression
19.35-1 (x(φψ) → (xφxψ))

Proof of Theorem 19.35-1
StepHypRef Expression
1 19.29 1495 . . 3 ((xφ x(φψ)) → x(φ (φψ)))
2 pm3.35 329 . . . 4 ((φ (φψ)) → ψ)
32eximi 1475 . . 3 (x(φ (φψ)) → xψ)
41, 3syl 14 . 2 ((xφ x(φψ)) → xψ)
54expcom 109 1 (x(φψ) → (xφxψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wal 1226  wex 1363
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 1316  ax-gen 1318  ax-ie1 1364  ax-ie2 1365  ax-4 1382  ax-ial 1410
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  19.35i  1500  19.25  1501  19.36-1  1546  19.37-1  1547  spimt  1607  sbequi  1703
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