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Theorem imdistani 442
Description: Distribution of implication with conjunction. (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
imdistani.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
imdistani ((𝜑𝜓) → (𝜑𝜒))

Proof of Theorem imdistani
StepHypRef Expression
1 imdistani.1 . . 3 (𝜑 → (𝜓𝜒))
21anc2li 327 . 2 (𝜑 → (𝜓 → (𝜑𝜒)))
32imp 123 1 ((𝜑𝜓) → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  xoranor  1359  nfan1  1544  sbcof2  1790  difin  3344  difrab  3381  opthreg  4515  wessep  4537  fvelimab  5524  elfvmptrab  5563  dffo4  5615  dffo5  5616  ltaddpr  7517  recgt1i  8769  elnnnn0c  9135  elnnz1  9190  recnz  9257  eluz2b2  9514  elfzp12  10001  cos01gt0  11659  oddnn02np1  11770  bj-charfundc  13383
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