Theorem simplbi2 367

Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011.)

Hypothesis

Ref	Expression
pm3.26bi2.1	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))

Assertion

Ref	Expression
simplbi2	⊢ (𝜓 → (𝜒 → 𝜑))

Proof of Theorem simplbi2

Step	Hyp	Ref	Expression
1		pm3.26bi2.1	. . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))
2	1	biimpri 124	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜑)
3	2	ex 108	1 ⊢ (𝜓 → (𝜒 → 𝜑))

Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm5.62dc  852  pm5.63dc  853  simplbi2com  1333  reuss2  3217  elni2  6412  elfz0ubfz0  8982  elfzmlbp  8990  fzo1fzo0n0  9039  elfzo0z  9040  fzofzim  9044  elfzodifsumelfzo  9057  ialgcvga  9890