Theorem simplbi2 385

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 133	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜑)
3	2	ex 115	1 ⊢ (𝜓 → (𝜒 → 𝜑))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.62dc  945  pm5.63dc  946  simplbi2com  1444  reuss2  3415  elni2  7312  elpq  9646  elfz0ubfz0  10122  elfzmlbp  10129  fzo1fzo0n0  10180  elfzo0z  10181  fzofzim  10185  elfzodifsumelfzo  10198  p1modz1  11796  dfgcd2  12009  algcvga  12045  pcprendvds  12284