Theorem simplbi2 382

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 132	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜑)
3	2	ex 114	1 ⊢ (𝜓 → (𝜒 → 𝜑))

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  929  pm5.63dc  930  simplbi2com  1420  reuss2  3351  elni2  7115  elfz0ubfz0  9895  elfzmlbp  9902  fzo1fzo0n0  9953  elfzo0z  9954  fzofzim  9958  elfzodifsumelfzo  9971  dfgcd2  11691  algcvga  11721