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Theorem a1dd 42
Description: Deduction introducing a nested embedded antecedent. (Contributed by NM, 17-Dec-2004.) (Proof shortened by O'Cat, 15-Jan-2008.)
Hypothesis
Ref Expression
a1dd.1 (φ → (ψχ))
Assertion
Ref Expression
a1dd (φ → (ψ → (θχ)))

Proof of Theorem a1dd
StepHypRef Expression
1 a1dd.1 . 2 (φ → (ψχ))
2 ax-1 6 . 2 (χ → (θχ))
31, 2syl6 29 1 (φ → (ψ → (θχ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  merco2  1501  ax12b  1689  nfsb4t  2080  lenltfin  4469  tfinltfinlem1  4500  xpexr  5109  eqfnfv  5392  dff3  5420  spacind  6287
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