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Theorem im2anan9 808
 Description: Deduction joining nested implications to form implication of conjunctions. (Contributed by NM, 29-Feb-1996.)
Hypotheses
Ref Expression
im2an9.1 (φ → (ψχ))
im2an9.2 (θ → (τη))
Assertion
Ref Expression
im2anan9 ((φ θ) → ((ψ τ) → (χ η)))

Proof of Theorem im2anan9
StepHypRef Expression
1 im2an9.1 . . 3 (φ → (ψχ))
21adantr 451 . 2 ((φ θ) → (ψχ))
3 im2an9.2 . . 3 (θ → (τη))
43adantl 452 . 2 ((φ θ) → (τη))
52, 4anim12d 546 1 ((φ θ) → ((ψ τ) → (χ η)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by:  im2anan9r  809  ax11eq  2193  ax11el  2194  xpss12  4855  f1oun  5304  fntxp  5804  fnpprod  5843  fce  6188
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