Theorem mpcom 32

Description: Modus ponens inference with commutation of antecedents. (Contributed by NM, 17-Mar-1996.)

Hypotheses

Ref	Expression
mpcom.1	⊢ (ψ → φ)
mpcom.2	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
mpcom	⊢ (ψ → χ)

Proof of Theorem mpcom

Step	Hyp	Ref	Expression
1		mpcom.1	. 2 ⊢ (ψ → φ)
2		mpcom.2	. . 3 ⊢ (φ → (ψ → χ))
3	2	com12 27	. 2 ⊢ (ψ → (φ → χ))
4	1, 3	mpd 14	1 ⊢ (ψ → χ)

Syntax hints:   → wi 4

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

This theorem is referenced by:  syldan  456  ax16i  2046  ceqex  2970  unsneqsn  3888  sfintfin  4533  0cnelphi  4598  vtoclr  4817  opeldm  4911  tz6.12-1  5345  tz6.12c  5348  fununiq  5518  oprabid  5551  eloprabga  5579  ndmovordi  5622  clos1conn  5880  enmap2lem3  6066  enmap2  6069  enmap1lem3  6072  enpw  6088  ce0nnuli  6179  fnfrec  6321