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Theorem simplbi2 383
 Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011.)
Hypothesis
Ref Expression
pm3.26bi2.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
simplbi2 (𝜓 → (𝜒𝜑))

Proof of Theorem simplbi2
StepHypRef Expression
1 pm3.26bi2.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21biimpri 132 . 2 ((𝜓𝜒) → 𝜑)
32ex 114 1 (𝜓 → (𝜒𝜑))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104 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 depends on definitions:  df-bi 116 This theorem is referenced by:  pm5.62dc  930  pm5.63dc  931  simplbi2com  1421  reuss2  3383  elni2  7213  elpq  9535  elfz0ubfz0  10002  elfzmlbp  10009  fzo1fzo0n0  10060  elfzo0z  10061  fzofzim  10065  elfzodifsumelfzo  10078  dfgcd2  11870  algcvga  11900
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