Theorem jctir 524

Description: Inference conjoining a theorem to right of consequent in an implication. (Contributed by NM, 31-Dec-1993.)

Hypotheses

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

Assertion

Ref	Expression
jctir	⊢ (φ → (ψ ∧ χ))

Proof of Theorem jctir

Step	Hyp	Ref	Expression
1		jctil.1	. 2 ⊢ (φ → ψ)
2		jctil.2	. . 3 ⊢ χ
3	2	a1i 10	. 2 ⊢ (φ → χ)
4	1, 3	jca 518	1 ⊢ (φ → (ψ ∧ χ))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  jctr  526  equvini  1987  uniintsn  3964  ltfinp1  4463  vfinspeqtncv  4554  foimacnv  5304  respreima  5411  fpr  5438  spacssnc  6285