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Theorem a2d 23
Description: Deduction distributing an embedded antecedent. (Contributed by NM, 23-Jun-1994.)
Hypothesis
Ref Expression
a2d.1 (φ → (ψ → (χθ)))
Assertion
Ref Expression
a2d (φ → ((ψχ) → (ψθ)))

Proof of Theorem a2d
StepHypRef Expression
1 a2d.1 . 2 (φ → (ψ → (χθ)))
2 ax-2 6 . 2 ((ψ → (χθ)) → ((ψχ) → (ψθ)))
31, 2syl 15 1 (φ → ((ψχ) → (ψθ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
This theorem is referenced by:  mpdd  36  imim2d  48  imim3i  55  loowoz  96  ralimdaa  2691  reuss2  3535  ltfintri  4466  spfinsfincl  4539  spfininduct  4540  funfvima2  5460  clos1conn  5879  leconnnc  6218  nchoicelem17  6305
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