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Theorem imim1d 69
Description: Deduction adding nested consequents. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)
Hypothesis
Ref Expression
imim1d.1 (φ → (ψχ))
Assertion
Ref Expression
imim1d (φ → ((χθ) → (ψθ)))

Proof of Theorem imim1d
StepHypRef Expression
1 imim1d.1 . 2 (φ → (ψχ))
2 idd 21 . 2 (φ → (θθ))
31, 2imim12d 68 1 (φ → ((χθ) → (ψθ)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  imim1  70  imbi1d  220  expt  582  hbimd  1462  moim  1961  moimv  1963  sstr2  2946  ssralv  2998  soss  4042  prarloclem3  6480  fzind  8129  iseqfveq2  8905  setindft  9425
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