Theorem jctr 239

Description: Inference conjoining a theorem to the right of a consequent.

Hypothesis

Ref	Expression
jctr.1	⊢ ψ

Assertion

Ref	Expression
jctr	⊢ (φ → (φ ∧ ψ))

Proof of Theorem jctr

Step	Hyp	Ref	Expression
1		id 9	. 2 ⊢ (φ → φ)
2		jctr.1	. . 3 ⊢ ψ
3	2	a1i 7	. 2 ⊢ (φ → ψ)
4	1, 3	jca 236	1 ⊢ (φ → (φ ∧ ψ))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  bm1.1 1088  unisseq 1946  supeu 2158  tfr3 2964  pssnn 3428  hlimreu 5145  hlimeu 5146  pjpj0 5259  shunss 5338

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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