Theorem pm3.21 471

Description: Join antecedents with conjunction. Theorem *3.21 of [WhiteheadRussell] p. 111. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
pm3.21	⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))

Proof of Theorem pm3.21

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜓 ∧ 𝜑) → (𝜓 ∧ 𝜑))
2	1	expcom 413	1 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))

Syntax hints:   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by:  iba  527  ancr  546  anc2r  554  19.29r  1874  19.40b  1888  19.41v  1949  19.41  2236  2ax6elem  2468  mo3  2557  2mo  2641  relopabi  5769  smoord  8295  fisupg  9193  winalim2  10609  relin01  11662  cshwlen  14723  aalioulem5  26260  musum  27117  chrelat2i  32327  bnj1173  34968  waj-ax  36387  sbn1ALT  36831  hlrelat2  39382  pm11.71  44370  onfrALTlem2  44520  19.41rg  44524  not12an2impnot1  44542  onfrALTlem2VD  44862  2pm13.193VD  44876  ax6e2eqVD  44880  ssfz12  47299