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Theorem spimvw 1669
Description: Specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
spimvw.1 (x = y → (φψ))
Assertion
Ref Expression
spimvw (xφψ)
Distinct variable groups:   x,y   ψ,x
Allowed substitution hints:   φ(x,y)   ψ(y)

Proof of Theorem spimvw
StepHypRef Expression
1 ax-17 1616 . 2 ψx ¬ ψ)
2 spimvw.1 . 2 (x = y → (φψ))
31, 2spimw 1668 1 (xφψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  cbvalivw  1674  spw  1694  alcomiw  1704
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