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Theorem im2anan9 563
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 ((𝜑𝜃) → ((𝜓𝜏) → (𝜒𝜂)))

Proof of Theorem im2anan9
StepHypRef Expression
1 im2an9.1 . . 3 (𝜑 → (𝜓𝜒))
21adantr 270 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 im2an9.2 . . 3 (𝜃 → (𝜏𝜂))
43adantl 271 . 2 ((𝜑𝜃) → (𝜏𝜂))
52, 4anim12d 328 1 ((𝜑𝜃) → ((𝜓𝜏) → (𝜒𝜂)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  im2anan9r  564  trin  3905  xpss12  4493  f1oun  5197  poxp  5904  brecop  6283  enq0sym  6736  genpdisj  6827
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