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Theorem a1dd 48
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 33 1 (𝜑 → (𝜓 → (𝜃𝜒)))
Colors of variables: wff set 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:  exmidsssnc  4126  nnsub  8766  difelfzle  9918  facdiv  10491  facwordi  10493  faclbnd  10494  dvdsabseq  11552  divgcdcoprm0  11789  exprmfct  11825  prmfac1  11837  bj-inf2vnlem2  13199
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