Theorem jctr 526

Description: Inference conjoining a theorem to the right of a consequent. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 24-Oct-2012.)

Hypothesis

Ref	Expression
jctl.1	⊢ ψ

Assertion

Ref	Expression
jctr	⊢ (φ → (φ ∧ ψ))

Proof of Theorem jctr

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (φ → φ)
2		jctl.1	. 2 ⊢ ψ
3	1, 2	jctir 524	1 ⊢ (φ → (φ ∧ ψ))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  mpanl2  662  mpanr2  665  bm1.1  2338  mpt2eq12  5663  ncspw1eu  6160  ce0nn  6181  lec0cg  6199  lecncvg  6200