Theorem ct1 57

Description: Introduce a right conjunct. (Contributed by Mario Carneiro, 30-Sep-2023.)

Hypotheses

Ref	Expression
ct1.1	|- R |= S
ct1.2	|- T:*

Assertion

Ref	Expression
ct1	|- (R, T) |= (S, T)

Proof of Theorem ct1

Step	Hyp	Ref	Expression
1		ct1.1	. . 3 |- R |= S
2		ct1.2	. . 3 |- T:*
3	1, 2	adantr 55	. 2 |- (R, T) |= S
4	1	ax-cb1 29	. . 3 |- R:*
5	4, 2	simpr 23	. 2 |- (R, T) |= T
6	3, 5	jca 18	1 |- (R, T) |= (S, T)

Syntax hints:  *hb 3  kct 10   |= wffMMJ2 11  wffMMJ2t 12

This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-cb1 29

This theorem is referenced by:  an32s  60  anassrs  62