Metamath Proof Explorer


Theorem bnj1241

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypotheses bnj1241.1 φAB
bnj1241.2 ψC=A
Assertion bnj1241 φψCB

Proof

Step Hyp Ref Expression
1 bnj1241.1 φAB
2 bnj1241.2 ψC=A
3 2 eqcomd ψA=C
4 3 adantl φψA=C
5 1 adantr φψAB
6 4 5 eqsstrrd φψCB