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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
StepHypRef Expression
1 ct1.1 . . 3 |- R |= S
2 ct1.2 . . 3 |- T:*
31, 2adantr 55 . 2 |- (R, T) |= S
41ax-cb1 29 . . 3 |- R:*
54, 2simpr 23 . 2 |- (R, T) |= T
63, 5jca 18 1 |- (R, T) |= (S, T)
Colors of variables: type var term
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
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